I only played bioshock 2, but It can't be that different. I think they're 3 main appeals to the bioshock games: tactical RPG elements, the atmosphere and of course the combat.
I liked the way i could choose the plasmids to work for my play style (shoot it till it dies, Im not that creative) and the whole, hacking combat drones, making big daddies help in a fight and hacking stuff, was a nice little distraction from the combat
The atmosphere of the game is something to comend. It feels dark and suffocating, like your at the bottom of the - oh wait yeah, you are - some of the things, like the little sisters, I genuinly wanted to do the good thing because the idea of killing this little girl for a few measly ADAM points made me feel sick. The big daddies and their creation spooked me and the big sisters from no.2 felt well, evil, i really wanted them to die.
The combat was fun, the whole use of plasmids was fun, sure it was a basic first person shooter, but hey! bees out of the hand, what could go wrong with that? not to mention all the non-combat plasmids, they were fun