I cannot say how it compares to next gem consoles, because I haven't played it there yet... But for the xbox360, here's what I see:
Season pass isn't working properly. No fix on this yet, so I'm waiting to buy it. If I get an Xbox one before then, I'll just wait to buy it on a next gen system.
Graphics are amazing! I've heard the graphics are almost on par with xboxone, but again, I can't say that for sure. I'd imagine the Xbox one is a little better polished, and has better gas/fire/water effects, but all that still looks really good on the 360 too! Same with lighting.
There are some minor graphical glitches here and there... Some times, objects apear to be floating, but really there's a crate under it or something which didn't seem to load. If you pause, then unpause the glitch fixes itself. Other times, it looks like the alien passes right through wall corners, or sticks it's face right through locker doors while sniffing for me, but not so often that it kills the experience (like with A:CM). Not sure if those same issues happen on next gen consoles or not.
My biggest grievance, with respect to performance, is the lag. Some times, if there's a lot of action/moving objects, the game starts to lag and it gets really "jumpy." For example, if I'm being attacked by 4 or 5 joes, who are all on fire, it'll start to lag. It's not too frequent though, so forgivable to me.
There are some lip syncing issues too, but I believe that's on all platforms. That's forgivable in my opinion too.
All in all, I can't wait to try it out on a next gen console, but even on the Xbox 360 I am very impressed and love this game! Best alien(s) game ever, in my opinion!