I found the game fairly narratively satisfying (yes, even the awful third ending) with a few exceptions. It was firmly tied to Arkham City and the events there, rather than ignoring the previous games.
Most of the Riddler's puzzles were genuinely interesting to figure out rather than being exercises in perfection.
I <3 Cash's comments about all the items in the evidence room.
The additions to melee combat and stealth mode were reasonable and added some challenge.
Not so good:
I know this isn't a Bioware game, so your choices don't really make any difference. But I hate it when it's pointed out to you that your choice doesn't make a difference by circling around again and making you pick the "right" choice. If you had to play the rest of the game as Robin instead, that wouldn't be so horrible, would it?
The villain's identity is not a secret to any informed Batman fan. Despite trying misdirection, which doesn't work in the DC universe anyway. Similarly, Barbara Gordon's death is unconvincing rather than tragic.
Just how Scarecrow finances this huge army of men and drones is never really clarified, even in the audio files. With multiple billions of dollars he could probably create fear at a large scale somewhere other than Gotham, much more efficiently.
Arkham Asylum and Arkham City take place in small, bounded environments and that's OK--- it even adds to the atmosphere. Arkham Knight takes you into the city proper (three separate islands) and still feels tiny. This is particularly bad when you're chasing somebody through the streets and they keep circling the same few blocks because that's all there is.
The "stealth" tank battles were merely tedious. I hadn't taken out all the watchtowers or roadblocks but it didn't seem like they coordinated. The antagonists should have been using one of their flying drones (kept in reserve) to spot Batman.
The running tank battles are fine (though I was annoyed because I didn't realize the Batmobile had a cannon for quite a while, which made puzzles that required the use of the big gun frustrating when I tried to solve them with the machine gun.) But the experience of driving the Batmobile made me feel like an incompetent driver, rather than experiencing what it would be like to be Batman racing through the streets. The hand-to-hand fights do a good job of putting you in the Batman fantasy. Tearing through the streets causing widespread mayhem, not so much. The amount of damage Batman does to the urban infrastructure is quite frankly unconscionable. It made me feel like I was playing Saints Row, not a Batman game.
The game's intro assuring you that everybody good has been evacuated from the city, thereby giving you permission to run rampant on the remaining citizens, is appalling. While the Batmobile has "non-lethal" features, I'm pretty sure some number of thugs I hit with the car would have died. Particularly the ones whose heads I parked on.
One of the things I liked about Arkham City was playing as Catwoman. Arkham Knight gives you two-hero battles in which you can switch back and forth between Batman and whoever's fighting alongside you (Catwoman, Robin, or Nightwing). Not only is this less satisfying, but you don't get enough time with an alternate character to really learn their combat moves. The melees are all "big", not giving a lot of room for experimentation. (It looks like the alternate-character content was moved into DLC, and the reviews of the DLC are not great.)