So I very much liked the game. The story in particular, especially in the finish, was very good in its content and pacing. I think they did a great job in changing some of the systems from the previous installments in the Bioshock series that wouldn't have worked as well in Infinite.
The addition of the skyhook and the rail-riding mechanics made the fights feel really alive and the two held weapons system, while hardly new, really fit into the faster pace of Infinite. The recharging shield felt very natural to add to the series and effectively alleviated the issue of basically just having ~9 hp bars like in Bioshock one and two.
Having said that, I feel that the slowness and lack of agility of Booker (the player character) lets down most of the strong points of the game. The skyhook jumping and fast traversal feels really good but then when you land on the ground again it highlights the seemingly subpar walkspeed.
The enemies are very fast, quite varied in their abilities and feel satisfying to take down but Booker's lack of mobility, speed and ability to gain momentum really limits how you can take them on. I ended up swapping between being stationary behind cover (which admittedly felt tactical and organic) and flying about on skylines like a hyperactive helicopter, neither of which seemed like a proper solution in the long term.
The Vigours (like plasmids from Bioshock one and two or magic equivalent) did offer a large variety of combat tactics but again the speed of the enemies in conjunction with Booker's heavy feet made trying to set up combos of status effects, traps and bursts of elemental damage feel like a waste of time.
All in all, the addition of some more 'modern' pop-FPS mechanics made the game feel much more lively and they were able to implement them very naturally into the experience, often difficult to do with these kinds of mechanics. Having a faster player character that was faster and more agile on his feet would have, in my opinion, significantly added to the newer systems in place.
Also airships are dope as hell.