I posted this on the Halo community OT, there is a large amount of BS fans on there.
I might as well add it here, I've added some stuff after playing some more. Specifically the tears and two weapon limit.
So here are my initial thoughts on it, I'm not going to say anything about the story.
The game itself is an incredible sequel, Irrational do many things in infinite that really resonates with me.
The first thing is that they have created a world, contrasting with rapture but built up with interesting characters and ideologies. They've populated it with grandeur and mystery far beyond what I thought was possible this gen.
Certainly it costs them, there is a regular occurrence of stuttering, although I don't think as much as you would get if you installed the disk (I have it installed). But, there is an ability to unlock the framerate to provide a smoother experience at the expense of graphical fidelity.
Everything else is top notch, you can see and hear style ooze throughout every inch of the game, the music sublime, the menu is awesome, I could just leave it on there for a couple of minutes.
Now, in relation to the gameplay, this is Bioshock through and through, yet, more polished. The most common criticism of BS1 was that the gunplay was quite poor. I think they've done a marvellous job to bring that up to scratch, it now plays as good you would expect from a traditional shoot bang game. The sky hook is a very thrilling and novel way to travel, and in combat situations, the whole game when using the sky hook, plasmids and guns, it just clicks.
Then there are tears, and these really open up useful options during combat, I'll explain one battle, it was the battle before the gondola ride, the whole place is set up to exploit, as I'm waiting to fight the men who enter the area, I quickly dispose of two before accessing the skyline, at this moment I'm getting pegged. So I ask Elizabeth to 'tear' in some cover, as I land behind it, I lay a crow trap. The men who were pinging me with bullets, give chase on the skyline, my health is low, Elizabeth tosses me a health pack, I get back on the skyline and go to a rooftop which contains a sniper rifle tear, Elizabeth calls it in, I aim to where I layed the crow traps to see men stumbling and proceed to literally snipe their heads off. Just glorious amounts of possibility.
In relation to the two weapon limit this is perhaps the first game since Halo ODST (and before that Halo CE), where I have genuinely had to pause and consider which two weapons will benefit me before entering the next area.
Two tips, if you want to maximise the better FPS mechanics you should choose the second controller option, which put ADS on the left trigger and plasmids on the LB. The second tip is that you should start the game on the hard difficulty, it is pretty easy so far.
Irrational have also delved into issues such as racism and religion with great depth, this is evident from how game presents such issues, either graphically or through audio diaries. They have confronted those issues, whereas other devs would shy away from them.
And as a last word, to those on here who are big BS fans, what can I say? Well, remember seeing Rapture for the first time? Exploring its wonder and mystery and being satisfied by it all? Well, be prepared to have that feeling all over again.