I think it's a combination of great graphics + ridiculous attention to detail (skin with marks, sweat, pores, etc) + just unmatched (IMO) animation. And this final bit is the "big one" for me.
The way the characters move, talk, look, breath...they LOOK and FEEL real. Like a person you could see on the train one day, really.
That's what I think really sets apart their games from similar ones graphically and in how they feel, if that makes sense.
Yeah I get you, you laid it out better than I could've.
No game has touched U4's animations since it came out, doesn't help I've seen way too much ME: A lately (different games I know!)
Now make the high quality ass gif from this.
Dunno why I laughed so hard at this!