The PS1 is the better console. Wii has a handful of the greatest games ever made, plus a bunch of excellent exclusive titles, but the PS1 library is just too huge, and too damn good.
Tomb Raider, Metal Gear Solid, Final Fantasy, the list goes on and on.
OT: This thread and the N64 vs. Xbox thread don't really provide fair match-ups. I'd like to see the winners of each thread go head-to-head, actually. Because N64 vs. PS1 is the most interesting debate, at least to me. I can't think of a single generational contest where each console is so closely matched.
Maybe the seventh generation.