Oh this one is easy.

Tough call. I like both equally

Jak and Daxter. I like the open world platforming (and the action that came with 2 and 3) as opposed to the just holding the analog stick forward and jumping =/.

Not saying that ND wouldn't make some new mechanics for Crash, but based on what we know from Crash vs Jak and Daxter, if I had to choose a proper sequel to Warped (Wrath of Cortex and anything beyond that don't exist to me) and a proper sequel to Jak 3 (Lost Frontier doesn't exist to me)......Jak all the way 

Yeah, I excuse Crash poor games because they were after had switched studios. That original trilogy was brilliant. Jak had a great start, but Jak II was a back step in nearly every conceivable way.  I would love to see another Crash, I am indifferent to more Jak.

Jak!

I'd go Jak. I don't see much chance of anyone topping Mario games when it comes to "regular" platformers... and even then it takes a lot for the Mario games to get my attention.