Everyone does a bit of both. You need to weight and unweight and the best surfers do both well. But.....
front foot - Taj Burrow, young Rob Machado, Adriano deUseless, Jeremy Flores (flicky, fast, snaps without gouges, no real power when compared to....)
back foot - Parko, Slater, Occy, Carroll, Garcia, Egan, Knox (hard gouging turns in critical parts of the wave, a heavier commitment to rail and really chucking their weight into the board via their backfoot).
Back foot surfing wins world titles. Always has, always will. Front foot surfing looks good in vids when they can edit out every second wave where they fell or wasted a wave.
Umm....does my bias show through here. But seriously, every world title pretty much (with the very odd exception) has been won by someone who knows how to lay serious rail.