I'm likely a little late on this and I'm not even sure where to start, but I'm about 5 or so hours in on hard.
At first Infinite feels immediately like Bioshock 1/2 with the whole introduction sequence among many other nods. However, Irrational slowly introduces new twists to existing mechanics and completely messes with your expectations from both a gameplay and story standpoint.
I'm slowly working my way through the game but I go very slowly as I'm the type who loves to explore all the small side areas just outside the main path and check out all the environment art. I think in another life if I had any sort of artistic talent - which I dont - I'd seriously consider becoming an environment artist. I'm absolutely in love with the look and feel of Columbia. So much thought and subtle details put into the world and all this immediately reminds of why I loved the original Bioshock so much. My only complaint so far is that I wish the levels had taken a more Hub based approach instead of the current rather linear layout. I'm still early though as the game just introduced the concept of tears so it's entirely possible the areas I haven't seen are wider in scope.
Also, the mechanics are probably the single biggest improvement over the both previous titles. The guns themselves feel significantly better than either previous Bioshock title. They've got a really nice weight to them and I like that I don't have to use iron sites 90% of the time to use them successfully. Also, it might just be my imagination but the vigors in this game feel more powerful than plasmids did in Bioshock 1/2. The ability to combo multiple vigors and traps also adds some nice wrinkles to the existing formula. I've only just been introduced to what tears are and I haven't had the chance to experiment with them just yet. I'm looking forward to seeing how that changes the way I approach the upcoming encounters.
I can't remember the last time I woke up early and put some time into a game prior to heading into work. Nice work, Irrational.