Different cosmology, different in-game history, no Blood War, the goofy 4e alignment system, etc.
IMO:
Cosmology: Semantics. Astral plane, astral sea, limbo, elemental chaos, above, below, in between, it doesn't matter.
In-Game History: "Clueless Prime" stuff + mostly unimportant legacy material. Sure, primordials and deities might be very important for the Clueless, but PS takes a broader view, where gods and primordials and demon princes and lords of the nine and whatever are all just part of one big "things you should not try to punch in the face" kind of being. A lot of the early 1e history and such, while interesting, isn't important to the play experience of Planescape, so I can see leaving that ambiguous: it's there if you want it, but there's not much of an impact on the current setting.
No Blood War: This is "advancing the timeline" plus the "clueless prime" stuff. There's an uneasy down-time in the constant war which may erupt frequently into all-out grand-scale warfare, just not frequently doing so on the Prime. As far as the Clueless are concerned, there's no blood war, but you'd be a fool to think that just 'cuz the Abyss ain't marching on Malebolge right this very moment that it means that everyone's all hunky-dory. In fact, this gives me a broader idea for making the fiends key antagonists in PS4e. Perhaps the yugoloths brokered a peace agreement in a scheme to unite the lower planes, and now they have to try and keep it together long enough to do something with it, while covert agents of Good work through adventurers to sew the seeds of conflict and rivalry in the armies of evil.
4e Alignment System: A savvy viewer sees that the 4e alignment system is just a slightly more abstract version of the alignment system 2e and 3e used. There are still beings of ultimate order and entities of eternal chaos, they just aren't called out as such in explicitly mechanical terms. I don't think the concept of, say, Bytopia hinges on any two-phrase keyword. It's personality doesn't change, and in 4e it's open to the forces of evil as well as the forces of (Neutral-Lawful) Good.
I think PS4e could work for these reasons, and I am looking forward to running a PS4e game at some point in the future.