I have both and much prefer my Teva Mush. I have several styles in the Reef: Sandy, several pairs of Ginger, Fanning, and Slap.
You might also want to look at the Montrail Molokini flip flops. I usually carry at least one pair of those with me every trip. They sortof look like some of the Reefs Slap or Fannings, but are much more comfortable. The Reef Ginger flip flops have very thin straps (sort of like the Teva Ulani). I would not recommend them at all for WDW. I love them for around here, but not for all day at the parks. Those narrow straps between the toes will kill you. The ones with the wide straps on top and the ribbon thingy between the toes are the most comfortable (Sandy). Both the Sandy and the Ginger's have the foam type bottoms, like the Teva Mush. The Slaps and Fanning's have a more solid sole like the Montrail Molokini's. I don't like them either though, because they have a more rough textured foot bed that bother my feet. If I was going to take a pair of my Reefs to WDW I'd go with the Sandy's. Again, personally I'll stick with my Teva Mush or even the Montrail Molokinis. (I don't like to wear my Teva Ulani's down there either, because of the thin straps)