There is quite some differences between the original PS3 game and the Re;Birth PS Vita game aside from mechanics. the basic premise of the plot is still the same but the progression though it and the finale are different
In the original game, much like Re;Birth, the 4 nations were on floating continents however in the original game they moved. this played to a mechanic where you had to go through dungeons in order for time to progress before one of the other nations where nearby for you to cross over. in Re;Birth it appears they don't move as the world map doesn't show them changing places
Also in the original game every dungeon was on it's own floating island which circled a nation so more or less the 4 nation's main continents were more or less a giant city. this isn't the case in Re;Birth with some of the dungeons being on the same landmass as a nation's capital
Alot of the elements of the main plot remain consistent between the 2 such as the quest to get the Keyfragments to release Histoire, IF being a fan of Vert and being used to poison Neptune. Avanir taking control of Lastation, Afoire's final plan to destroy Gameindasti by colliding the 4 nations and Green Heart proudly boasting about her breast size to Lady White Heart at the beginning prompting Lady White Heart to call her "Thunder Tits". however the events within the main plot have been changed up
in the original game all 4 Key Fragments were guarded by the Guard Vermin, one in each nation which only was accessible after the 2nd Arc of Lastation, Lowee and Leanbox. Planeptune's Keyfragment acquisition was still different as indicated in the screenshot as it was this dungeon that is shown in the Screenshot that the Keyfragment was obtained and it wasn't accessed by Neptune and Compa falling down
Missing Characters in the Main Plot
Absent from Re;Birth was Nisa and Gust who represented their titler companies, Nippon Ichi Software America (the American branch of Nippon Ichi Software) and Gust.
In regards to Gust when Neptune was poisoned it was her who created the antidote thus her being removed also meant that this part had to be rewritten
Nisa was largely unimpressive and didn't leave much impact but a couple of character's background had to be re-written with her removal which we'll get back to later
Missing DLC Characters
while optional in the original game the 2 DLC Characters, Red and 5pb. (likewise named from their companies, Red Entertainment and 5pb.) both of whcih more focused on IF than Neptune
with Red she was looking to build her harem of "Wifeys" (english-fied version of waifu?) and targeted IF first. despite being defeated she kept trying to make IF, Compa and Neptune her Wifeys which always lead to a battle and her defeat.
with 5pb it starts off with her being shy about singing in front of people until IF find her and after a number of encounters builds up her confidences. 5pb also is shown to have a demon and angel side to her when she was contemplating stealing Neptune's puddling
in Re;birth the DLC characters are Histoire, Plutia and Peashy however the last 2 don't have any storylines associated with them (like why they have crossed to another dimension) while Histoire's "story" can more or less be the main plot as the DLC doesn't add her to the party until she is released (the later 2 are unlocked in chapter 1)
in the original game there were also other small substories consisting of a scene. some of these poked fun at other games such as Neptune, Compa and IF making comments on a Mario Cart like racing event.
One of Nisa's substoires involved her meeting with the Large Breast Loving Brothers however in the original game the Brothers were bandits. after getting into some trouble with monsters Nisa saves them after they ridicule her of her lack of breasts. when they question why Nisa did this after they ridiculed her, in her usual fashion Nisa boasts about her strong sense of justice and will always help those in need. moved by this the Brothers then turn over a new leaf. as Nisa is mission from Re;Birth the Brother's background was rewrote.
Another of Nisa's substories involved her helping a couple of people who were being chased by a Demon which was revealed to be a pissed off Lady White Heart who wanted to kill them for making fun of her chest size. Nisa calmed Lady White Heart down but when the people she was chasing thanked Nisa while at the same time making fun of her chest size (calling her pimple nipples if i recall) prompting Nisa to do a 180 and aid Lady White Heart to kill them (not sure if they were killed or just badly beaten).
another substory involved Lady Blanc and Noire both going to a convention in Lastation and seeing one another but not recognizing each other.
Because of the game mechanic in the original game where you could only traverse between continents when they were close the plot was broken up to be played in almost any order.
before getting the Keyfragment each nation had 2 Arcs. i says 2 because Leanbox was 2 distinctive plots but when i played i first went to Lastation and was forced to stop helping Chian and then went to Lowee (the continent cloest at the time) and was forced to stop that until i did Leanbox's first arc before returning to Lastion and getting the Keyfragment.
Lastions 2 Arcs were more or less the same with Avanir taking over Lastion, Noire feigning amnesia to lean why Neptune was there, helping Chian for the expo and fighting the CPU Breaker Avanir created.
I can't remember much of Lowee's Arcs but i think it was still similar as the CG on Blanc with a book in Re;Birth is also in the original game.
the first arc of Leanbox in the original game was more or less the same minus Vert joining the party and getting a Keyfragment. the second Arc was about Vert working her hardest to earn back the faith of her people after being lazy in the first Arc however was overheating alot (the X-Box 360 Overheating Problems when it was released) and being rescued by Neptune's Team (primary because IF was worried).
The Quartet Weapons
In the original game each weapon was on each continent but broken into 4, found at the end of 4 different dungeons which were all "kill the boss at the end" types so you had to go through 16 dungeons before being able to get to Celestia.
Also after remaking the 4 weapons Neptune leaves the party in an attempt to face Arfoire alone (having regained her memories) forcing IF, Compa, Gust and Nisa to fight her when they try and stop her.
in Re;Birth the weapons aren't broken and get remade into weapons that better suit the CPU. this also means that the CPUs didn't force the weapons into their sockets. also in the Original game the gateway worked so there was no need for the party to get the Basilicon's help
Also in the original game the acquisition of these weapons didn't coincide with each nation having to deal with Fake CPUs and thus Lady Blanc's 3 sizes was never blurted out during a quiz
in the original game the Guide was made up of people who were born in one nation but worshiped another's CPU. generally these people were looked down upon by others so IF's affiliation with the Guide was kept hidden for much of the game
in the original game the CPU's were optional, only required to get the True End. in order to get them using Gust's hidden ability to show the national share levels one needed to increase the shares for one nation in order to trigger an event which lead to Neptune, Compa and IF fighting them.
IF x Vert
IF's and Vert's relationship is much more expanded on in Re;Birth than it is in the original game, most likely because of how the CPU's are optional. in Re;Birth we see events such as Vert joining the party when they leave Leanbox stating she can't live without her Iffy, Vert using IF as her "warmer" in Lowee (placing the warmers IF gave her in her endowments before returning to her Iffy) and IF "dying" when everyone tried to fit into the portal device to transport them to Celestia with Vert, purposely, squeezing in with IF and smoothing her within her breasts. (to be honest i loved all these Shoujo Ai/Yuri moments between them. great improvement)
In the original game Overload Momus did not exists, same same in Re;Birth, however Arfoire never creates it. instead spreads the rumor that the CPU's fled Celestia when Overlord Momus appeared and destroyed it while also spreading news that the Overlord would descend from Celestia and the CPU's, now weakened, will not be able to stop it.
In Re;Birth Overload Momus takes the form of CFW.Arfoire from Hyperdimension Neptunia Mk. II (and i assume Re;Birth 2 as from what i have seen i don't see that the plot has changed), the form of the Deity of Sin Afoire takes when ASIC succeeds in resuecting her
DOS.Afoire, the Deity of Sin's true form, also appears in Re;Birth as a couple of Colosseum battles such as Delphinus (who too appeared in Mk. II's Colosseum as a palette swap of of DOS.Afoire however was a different pallet swap to Re;Birth's Delphinus)
in the original game it's revealed that Afoire was the True Goddess until she got tired of the job and split her power, and Gamindustri into 4, creating the CPUs and giving full control of the world to Histoire. later however she wanted it all back and reclaim her spot as the True Goddess and turned on Histoire and sparked the Console Wars so she could reclaim her powers from the CPUs.
in Re;Birth it's revealed that Afoire was just a regular human who fought along side the Hero Quartet when they fought the True Goddess who was evil. when the True Goddess was defeated her power was split into 4 and Arfoire raised the CPUs herself.
it is also initially suspected that Arfoire was corrupted by the True Goddess's power she copied from her during the battle and sought to become the new True Goddess however in Re;Birth's true end Nepture suspected that
Arfoire wanted to become the True Goddess so she could better raise the CPUs.
The 2 Endings, Normal and True, also are different.
I never got the Normal Ending in the original game however compared to Re;Birth's normal ending i can assume they would be different as one of the requirements of the True End in the original game was having all the CPU's (shares didn't count)
After defeating Afoire and escaping Celestia the CPU's realize they still have alot of work to do as Afoire's Enemy Disks are still active and all over the world. in order to make their job easier they sacrifice their HDDs making them regular humans and ridding the world of monsters for good
Afoire is defeated and Histoire visits each nations to see how the CPUs are doing finishing with Planeptune where she joins Neptune, Compa and IF in eating pudding
Afoire is defeated but tries to destroy Celestia. with the CPU's exhausted everyone goes to flee yet Neptune remains hoping to save Afoire with everyone having escaped but prays for Afoire to be saved too.
A Year later Histoire states that while everyone escaped Celestia was suspected to have been destroyed in the explosion, Neptune and Afoire with it, as the gateway no longer worked.
after visiting the other nations to see how the CPUs were doing she visits Planeptune. while IF and Compa are talking about Neptune, low and behold Neptune falls through Compa's roof revealing that Celestia wasn't destroyed but instead just the gateway and that she fell from the sky because she was flying around in HDD and got hungry and reverted back.
Neptune also introduces Afoire who was saved (and looks very different now not looking like some witch). Afoire apologies to Histoire about the trouble she has caused and voes to make up for it until the end of her life while Compa and IF warmly welcomes Neptune home
The CPU Candidates
if one got the Shares up to a certain level for Planeptune, Lastation and Lowee they can get plans to unlock Nepgear, Uni, Ram and Rom. to actually unlock them one had to get the items and the shares to 35% for the CPU Candidate's nation (which stills fall into the requirements for Re;Birth's True End which is 0% for Other Shares and all 4 nations having atleast 20%). following their unlocks there is a scene which Histoire says that they are born from the accumulation of shares with each CPU posting on their blogs about their new sister(s) (with Vert expressing how she's depressed that she didn't get one but will still work hard for Leanbox)
since i never got the normal ending in Re;Birth with any of the CPU Candidates unlocked i can only assume their appearance in the normal end is similar to the True End in which it appeared their small segment are injected in the scene with some differences as
with Nepgear she has taken over her sister's work since Neptune didn't return from Celestia
however how the world is formed in Re;Birth still makes it incompatible with the 2nd Hyperdimension shown in the other Re;Birth games and Megadimension Neptunia VII