Flite baseplate has two densities of EVA foam, but less of it surrounding the baseplate than the contacts do.
Contact Pro has four different with the same amount of foam surrounding the baseplate as the Contacts. So you have less of the baseplate touching the board than the Flite, which leads to truer board flex (something being a n00b, I can't really tell you about).
I've never ridden the Flites so I don't can't really comment. But, I had the Contacts and Contact Pro Baseplates both are EXTREMELY comfortable and I'd go with the Pro if you've narrowed it down to those two.
Like Shralp said though, if you want more response than your forces (I also have those), I'm pretty sure either of those are not going to give you that. I'd take his suggestions.