The Paul with single coils, hands down. Fenders with humbuckers sound cool, but to me, Les Pauls with single coils are the best sounding electric guitars ever made, in general. Pre-'57-style gold-tops and Customs; there's nothing like 'em!
My money is already where my mouth is. LP Goldtop with P90s. LP Junior Special with, you guessed it, P90s. Modified PRS (USA) EGII with three humbuckers. Still sounds very Stratty. I am also keen on Fenders with Filter'Tron style pickups.
Strat with humbuckers. It's what I use right now. Splitting the pickups sounds close enough to true single coils for the single coil funk/blues sounds I want, and you still have that thick humbucker sound for singing leads/harder rock sounds. Plus longer scale necks are better . . . AND if you decide you want to go to all singles in the future you just buy the pickups and swap out the pickguard.
I have several 2HB Les Paul guitars and many G&L Legacy (Strats), but I LUST for a '54 or '56 Gibson Historic Reissues (R4 or R6), or a LP Special Reissue.
The 2HB Fat Strat or "Big Apple Strat" doesn't do much for me.