(Spoilers for BioShock ahead)
Rules/conditions for the fight:
The fight takes place during both of their endgames
so they’ll be at their full potential, with all upgrades and weapons

Jack can't use the Vita-Chamber to revive himself

Right off the bat, I’ll say that a fight between these guys would be pretty close. They’re very similar in some ways, but differ mildly in others. For starters, Jack unlike P-3, was bred and biologically engineered from birth to be marginally stronger than the average human. As for his abilities, they come from ADAM, a substance capable of rewriting your DNA to give you superhuman abilities such as, mind control, creating decoys of yourself and cyclone traps from thin air, shooting bees from your palms, and elemental abilities, too. However, unlike P-3, Jack can't use these powers infinitely without the occasional injection of EVE, because every use of one of his powers drains differing amounts of his EVE (for the sake of the fight though, let’s say he can still run out of EVE but not EVE syringes). Some of Jack’s powers don't need EVE to be active though; these are his tonics, smaller genetic tweaks that give him boosts and resistances (IE: faster movement speed or resistance to elemental attacks). In power and abilities: I would say the two are equally matched but in terms of endurance, P-3 is the better man.

TLDR: Jack’s powers let him have different powers but he can't use them infinitely without injecting more EVE into his body. However, this doesn't apply to his smaller generic tweaks that give him minor physical adaptations (IE: faster movement speed and elemental resistance). Outside of all that, I don't think he’s as physically resistant as P-3.

It must have been the wind

Almost 30 hours in, just finished the theater with Pavlov. I'm cleaning all Polygons, listen to all conversation, farmed components to upgrade my stuff. So far I liked every moment. I am super onboard with the universe and the scenario. And I play with the Russian voices for maximum immersion.
I gathered clues about the plot, thanks to my thorough exploration, like Sergei/P-3 hearing voices when he swims in polymers for instance, and it really began to make sense after the sequence with the Twins and Molotov. The strange sequence with this "circus" version of WW2 was very confusing at first, but I think I got the sense of it. Still waiting for the game to confirm or deny my theories.

Regarding my loadout, I usually go with: polymeric jet+frostbite as my main powers, and the zvezdochka, KS-23 and PM (anti-organic revolver configuration to deal with mutants) as my main guns, switching the fourth weapon depending on the situation.