765 feels lighter, has better steering, it's more go-cart like. P1 has the unreal sound of the blowoff (way cooler sound), feels more immediate in the acceleration response (although ultimately I don't think there is really anything in a straight line between them), and probably feels more special. The 765 wing dances a lot more than the P1 wing does adjusting to driving conditions. The traction control of the 765 feels more advanced, how the car clings to the road and inspires confidence. The P1 requires more respect. It's scarier. It's a more immersive and full on experience overall. Like all Mclaren's though, driven slow, they're pussy cats. You just can't bury your foot whenever you feel like it.
As far as construction, the P1 is genuinely like an alien space ship. It bares little if anything in resemblance (both above and beneath the skin) to other Mclarens. The 765/Senna/720S are all very similar. Money no object, P1 all the way. But certainly driving them both you'd think the 765 is the greatest bargain currently on the market. I think the 765 should be trading hands for 900k-$1mm. If it wore a Ferrari badge it certainly would.