I'd be interested.
To start it off, there's a lot of aspects that really cannot be compared. The combat mechanics are apples and oranges. The first game had slow paced, tactical engagements which was all about figuring out how to stay out of harms way and use the environment to your advantage. Big fights with big daddies (and sistahs if you count 2) was done best by laying down mines, drawing them into turret fire, and choosing the right ammo.
The combat in Infinite is much more about getting an overview of the larger area. You use the lines and the tears to get to high ground and behind cover, you use speed and superior firepower (and vigourpower) to distract, flank and destroy large groups of enemies. You are, to a much larger degree, able to soak up some bullets, especially late in the game with the bulletblocking vigour. You do not have time to carefully plan - when something big comes up, you have to think on your feet, run away, and do chip damage until it's brought down. The goals are different, the tools are different, the pace is different. You can discuss which is better, but that would be more about if survival gameplay is more fun than fast-paced shooting gameplay.
Not to spoil anything, but both have largely unnecessary and not very interesting end bosses. The fight towards the end of Infinite is really fun, but not really something I felt was appropriate to end the game with. The bullet sponge you shoot at for two minutes until it dies at the ending of the first was neither really that fun, but it was a more necessary part of the story. What was the end fight for Bioshock 2? 2 big sisters at once? Creativity!
You'll probably be interested in talking about the story too, and I'll let someone else start off there, but an interesting note; you know how there's a big binary choice throughout the entire first game (harvest vs save) which leads to one of two different endings? And you don't have the same kind of split ending in Infinite? This is a quote about the first game from Ken Levine, the lead designer, I shamelessly stole from wikipedia: "it was never my intention to do two endings for the game. It sort of came very late and it was something that was requested by somebody up the food chain from me."
It's kinda funny how "choice" has become a selling point that's ticked off on a list of "things to make the game sell".
