Personally, I'm not too sure about 3d models in anime; sure, Appleseed has some very nice eye-candy shots, but the majority of anime that use this end up having way too simple models with really jerky animations. It looked awesome in Reboot because it was positively ground-breaking at the time, but when a movie is released nowadays but looks even worse than that, it goes beyond 'artistic style' straight into the 'crap' territory. At least, from what I've seen with my own eyes - can't say I'm knowledgeable on the subject.
On the topic of character design, in a good deal of cases my answer for that would be "Ep. II" simply because I found the eyes' placement a bit too wide on many faces in both Ep. I and III. At first I thought there was some kind connection between how a character looked and their role in the story (proportions seem wrong => the character was 'adjusted' biologically in some way) but I haven't been able to find any concrete evidence of anything like that.
As for the games themselves... I don't have much to nitpick about the 'dungeon' areas, but the vast majority of non-combat locales were criminally small, in my opinion. "A narrow corridor with a liberal amount of cutscene triggers thrown in" is a common complaint I believe.
It is certainly not the first (nor the last) game to be made this way, it could be even argued that there is not much deviation to be had from this approach when making a JRPG, yes. But! Can you remember, let's say, FFVII? It could be called a 'corridor with cutscenes' too, but did it seem that way when you first played it? Why more and more games seem to follow the FFX approach - an even more blatant case of linear level design than Xenosaga - and not FFVII?
Why is it when I want to play a game that lets me roam the landscape even a tiny little bit I have to load up Skyrim, Far Cry 2, GTA, Space Rangers, Gothic and the like but the Xenosaga universe - a setting that certainly looks like it has enough things to tell me via exploration alone - leaves me with tiny cramped spaces the size of my flat?
Gloriously detailed cinematics don't add even a one-tenth of gameplay value even one solidly built 'town' area would - a much better way to spend those gigabytes of disk space, I'd say. Or even just enough space to make the party characters no longer sit around on their hands when their comrades are getting butchered right in front of them, for christ's sake! There is also absolutely no need to voice-act every single line of dialogue in this kind of game either, those are just a huge sink of time, money and space that could spent elsewhere.
Xenosaga has too much 'Worf Effect', to use tvtropes' lingo. Those scenes where hundreds of ships with untold amount of faceless mooks get blown up by the newest Death Star equivalent? ~95% of them could be thrown out and nothing of value to the narrative would be lost. A party member gets a faceful of bullet? They'll be fine, nothing to worry about - unless they happen to be Ziggy or KOS-MOS, of course. But even in their case, did anyone in the audience doubt that they'll be rebuilt anew just in time to tank the next thrashing?
Those would be the things to be looked at first and foremost if Xenosaga Ep. I-III were to be remade, in my opinion.
As for something completely new... I'd say it could be cool if those spin-off games meant to fill the gaps via one specific character's POV instead of the party as a whole played differently.
For example, investigation work interspersed with bodyguard duty, infiltration and simply all-around 'tactical espionage action' Ziggy and/or Jin are likey to get involved in could play like Deus Ex / Thief / Splinter Cell / Dishonored / whatever.
Rubedo's part, depending on whether he'd go in alone or would command a platoon's worth of (mecha)nised infantry, would play either like bona-fide Max bloody Payne or turn-based (Front Mission?) / real-time (Ground Control?) tactic game. Or maybe something in-between in terms of scale; let's say small squad based counter-terrorist action akin to SWAT or Payday.
KOS-MOS would need some serious vertical freedom of movement if she ever starred in an action game. Whether it'd take the form of 'climb anything' like how Prince of Persia (the newer ones) / Assasin's Creed / Mirror's Edge do it or some sort of 'super jumping' like some of the Armored Core games or something, I don't know. If there would be some open field mecha action involved, Gun Metal could serve as inspiration.
Guilty pleasures like wishing for a Xenosaga fighting game akin to Guilty Gear?
Well, first off a good ol' beat-em-up like Street Rage or Golden Axe but spruced up with capabilities of modern systems is, in my opinion, an obvious option.
Something like a VN but with actual gameplay other than reading heaps of text would be nice, IMHO. Sengoku Rance comes to mind (in terms of how the game's event system works, not the abundant H-content).