The author, Kawahara Reki, didn't clearly say whether they are in the same timeline or not. During the Sakuracon Festival Interviews, he answered like this:
When you were creating the Alicization arc in Sword Art Online, was the technology used in the Alicization arc carried over as a foundation to Accel World?
It is true that the technology used in ...
They are in the same universe. Sword Art Online's Nerve Gear was elaborated in Accel World as a precursor to the implants seen in Accel World.
Anything further than that is likely speculation, until either light novel reveals more details.
There is a crossover, but it is still just a Special Chapter called Versus. It is just a fight between Kirito and Silver Crow, caused by a special dive machine. You can read a english version here.
Kazuto (Kirito) was on a part-time job to test out the 4th generation FullDive machine created by Rath. He was told that other users had seen a ghost and so he ...
It seems not to be some kind of "rule", but aspect of specific stronger abilities/avatars:
it was explicitly said that Black Lotus avatar inflicts permanent damage with her blades
"steal" ability wouldn't be much of a steal without permanent aspect to it
I don't think it was explored (in anime at least) if there are ways to purposely achieve it (from ...
In Accel World S1E22 ~17:00, the main character is doing some research which references the NerveGear.
NerveGear : The first VR Machine of the 2020's
Therefore, the story timeline place Accel World after SAO.
Combined with various Wikipedia articles, chronological order of the Anime is:
Sword Art Online
Sword Art Online Extra Edition (...
Accel World came first. According to their Wikipedia pages, Accel World light novel started in February 2009 while Sword Art Online started in April 2009. If you are referring to anime release, then the same can also be said since Accel World anime started airing in April 2012 while SAO anime started airing in July 2012.
As pointed out by @Memor-X, some ...
Dusk Taker (Nuomi) ability Demonic Commander can't be considered a ability that deals some kind of "permanent damage" but more like "ability transfer" or "ability taker", for that reason Demonic Commander doesn't deal any damage, and while my memory about the Anime is hazy, I'm pretty sure that the HP bar of Silver Crow (Haruyuki) didn't decreased and that ...
Actually, Accel World the anime 1st season covers Volume 1-4 + two short histories from Volume 10. (possible spoilers at the end)
Is important to notice that the two OVA's are not part of the main Light Novel series.
There's also a crossover drama CD. The second disc adapts the "Versus" storyline mentioned in Astral Sea's answer; the first disc is just two separate storylines (one for AW, one for SAO) with no crossing-over.
Sword Art Online was first. Kawahara originally wrote SAO in 2001 for a Dengeki Light novel contest, but due to exceeding the contest's page limit, he posted it online in 2002 under the pseudonym "Kunori Fumio". The story eventually concluded (with the Alicization arc) in 2008.
Afterwards, he decided to re-enter the same contest with what would later be ...
Another point to add to this that I have yet to see is that when Haruyuki was looking up the older generation tech, they show a picture. At first glance, I saw the similarities, and it was when he actually said "Nerve Gear" (in Episode 22) that I freaked.
I'm not saying that it's definite that it's connected, but really, it's totally possible. At the end ...