Just finished up the main story (minus acquiring the true ending). Overall enjoyed the game a lot more than I thought I would. I probably should qualify that by stating I really liked Asylum and City, and I certainly was looking forward to playing Knight quite a bit (to the point I didn't want to wait for the PC version to get fixed so I got it refunded and played it on console). And while I was certain Knight would be a good game, I was skeptical if the series truly had enough in the tank (forgive the pun) to deliver another game that matched the overall quality of it's predecessors.
While Arkham Asylum's atmosphere and setting are perhaps the best of the series (playing in a Gotham populated with civilians potentially could've been great as well, though I can perhaps understand their reasons for not going that route), I do like that Arkham Knight polished and improved upon the open world setting that Arkham City started. It isn't the massive open world that certain RPG's can claim, and certainly not all content in here is quality, but there's plenty to do and much of it is fun IMO. Watchtowers and Checkpoints for example feel reminiscent of Far Cry's outposts and share their addictive qualities of "let me just clear one more".
As far as the main story, opinions certainly will vary widely on it, but it was another thing I wound up liking a lot more more than I thought I would. Not sure where I'd rank it among the whole series, but I probably liked it more than City. But I haven't hit the true ending yet, so maybe my thoughts on it are a bit premature at this point.
The Batmobile appears the most controversial aspect of the game. I personally disliked it quite a bit in the beginning, particularly because it felt like it handled so poorly. But then I read somewhere that you shouldn't touch the right stick to adjust the camera while in pursuit mode (i.e. let the camera adjust itself) and the handling controls instantly became so much better. I went from sheer frustration in trying to do the "Gotham on Fire" and chase APC missions to actually having a lot of fun completing them, because I was no longer fighting the batmobile to get it to do what I wanted. I still think some of the acrobatic controls (i.e. doing loops to avoid obstacle or driving sideways through pipes) were a bit wonky, though thankfully most of that seems relegated to Riddler side content I'm more than happy to ignore.
I'm glad I learned that trick with the Batmobile controls, as I'm certain the game as a whole would've been a good deal less enjoyable for me if it remained such a struggle to control the thing. While I still spent most of my traversal in the city by gliding, I'm glad I was able to enjoy using the Batmobile as well.