I haven't heard about the “GITS: Arise − Border” movies you are talking about (I assume this is what the american licensee decided to call the Arise movies), but the storylines of Arise and Arise: Alternative Architecture overlap. If you already watched the longer Arise movies earlier, then you can skip the episodes 3-8 of AA which are basically the 4 movies split up into two part episodes. I did not do an extensive scene-by-scene or frame-by-frame comparison for all the episodes, but I watched them all in the order they aired and didn't notice any new scenes being added in AA.
I started comparing both versions of Ghost Pain yesterday in a video editor (kdenlive, one of the free editors that supports to show individual frames in the timeline) and got to about 13 minutes playtime until I gave up due to lack of skills to compare both efficiently and provide a usable result. What I found so far is that scenes have been re-arranged and shortened for AA: some scenes have been left out, while some stills appear longer on screen. The first scene in AA for example with the major at the airport in Ghost Pain was originally further in the episode/movie, scenes including dialog with Aramaki (at the cemetery) and Kurutsu (in her office) have been shortened.
Comparing runtimes of the movies and AA episodes it's
2*24m, so you're likely to watch an abridged version of the movies, where roughly 10 minutes of content had to be cut to meet the length required for the television broadcast edition. My guess is that the focus for creating new content was on the episodes Ghost Stands Alone (1, 2), Pyrophoric Cult (9, 10) and the new movie (see below).
If you haven't watched any of this, you probably want to watch in this order: Ghost Stands Alone (AA), Ghost Pain (Arise), Ghost Whispers (Arise), Ghost Tears (Arise), Ghost Stands Alone (Arise), Pyrophoric Cult (AA), New Movie.
Koukaku Kidoutai Arise: Ghost in the Shell
22.06.2013 till 06.09.2014, each episode is about 60 minutes long:
- Ghost Pain
- Ghost Whispers
- Ghost Tears
- Ghost Stands Alone
Koukaku Kidoutai Arise: Alternative Architecture
05.04.2015 till 14.06.2015, each episode is about 25 minutes long:
- Ghost Stands Alone, Part 1
- Ghost Stands Alone, Part 2
- Ghost Pain, Part 1
- Ghost Pain, Part 2
- Ghost Whispers, Part 1
- Ghost Whispers, Part 2
- Ghost Tears, Part 1
- Ghost Tears, Part 2
- Pyrophoric Cult, Part 1
- Pyrophoric Cult, Part 2
Koukaku Kidoutai: Shin Gekijouban
This is the new movie with a new story set in the Arise universe