The following reviews are all for the PS4 version, except the one from The Escapist (XBO)
Polygon (10/10): Arkham Knight is Batman perfected
Rocksteady has said this is its last Batman game, and I'm praying to the New Gods that they're on the level. After Arkham Knight, trying to find more meat on the Batman bone would define futility. After Arkham Knight, Batman has been perfected — and the end result is the best game of this console generation.
VideoGamer (10/10): Batman: Arkham Knight is not only the best Batman game ever made, but a game that will be remembered as exemplary. Obviously being a fan of the license is going to help no end - the Arkham trilogy as a whole is as important and impactful as its filming equivalent - and how this will ever be topped in terms of donning the cowl and being Gotham's protector is anyone's guess. But even those who don't frequent themselves with Bruce Wayne and his many adventures will still walk away feeling they've experienced something special.
It's epic; it's grand; it's addictive; it's ridiculously good-looking and it's going to be remembered for a long time to come. A masterpiece.
GameInformer (9.5/10): At the end of it all, Batman: Arkham Knight delivers a great sense of closure for this series. Rocksteady leaves a few plot threads dangling to tease and taunt us, but the grim tale that started all the way back in Arkham Asylum is done. I walked away from Arkham Knight shocked, satisfied, and in dire need of someone to discuss the story with. Rocksteady built a special experience that dazzles with its cleverness, intelligence, and ability to shift from kick-ass Batman moments to emotional gut punches to scenes stripped straight from some of Batman's greatest comic book stories. Lock yourself away, avoid social media and friends, and finish this game. You won't want this one spoiled for you.
IGN (9.2/10): If this is in fact the last Rocksteady-developed Batman game, the series will end on a high note. Arkham Knight is the biggest Batman game yet, not just in map size, but in the wide range of different types of gameplay, and its collection of characters. The addition of tank combat thematically clashes with everything Batman stands for, but it is fun, and having access to the Batmobile for the first time gives us a new world of possibilities for interacting with Gotham City. Arkham Knight is an outstanding game on almost every level.TheEscapist (4.5/5): The game performs well, but required a large day one patch - about 3.5 gigs - to function. Bugs were rare, but present, including two hard locks that crashed the Xbox One during my play through. Both occured during a key event that changes the face of the city, so it's unclear if that was their cause, but because the game frequently autosaves even in the open world I didn't lose any progress either time. An occasional bug caused enemies in stealth segments to forget they saw batman mid-fight, but that was rare and more amusing than troubling.
GamesRadar+ (4/5): Once I put a bit of distance between the campaign’s problems and the more positive experience of patrolling Gotham and mopping up these hours of sidequests, I really started to love Arkham Knight. I can see players just dipping in and out of this world forever, jumping in the Batmobile to chase down some criminals, visiting the villains in the lock-up at GCPD, gliding from an airship onto the LexCorp building; just being Batman in this worthy depiction of his universe.
GameSpot (7/10): What Batman: Arkham Knight does well, however, it does really well. Gotham is a dazzling playground where neon lights pierce through the rain and mist; all it takes is a single glimpse to tell you that this is a city in need. Moreover, many individual elements are so carefully constructed, and presented with such flair, that appreciation is the only reasonable reaction. Yet most of these elements--excellent acting, wonderful animations, moody soundtrack--are ones that Batman: Arkham City also excelled in, making Arkham Knight's missteps all the more noticeable. Rather than escape the pull of the games that spawned it, The Bat's newest adventure refines the fundamentals; it is a safe but satisfying return to the world's most tormented megalopolis.