I'm not an adventurous girl, nor have I ever felt the need to prove myself. Because of this, I've not engaged in any kind of extreme sport (eschewing all regular sport as well).
If I had to pick, though… I would much rather be skydiving than bungee jumping. Sky diving seems serene –seeing the world in a new way. There's something about the eventual float to earth that appeals to me. Sky diving, after the initial jump, seems almost serene.
Bungee jumping, however, looks like something the Spanish perfected during the inquisition. It seems so confining, and the appeared sensation of repeated falling and jerking doesn't appeal to me. I'm quite amazed that the jumper doesn't end up rebounding into the bridge. Something about the up and down, rubber band effect, nauseates me just as a spectator. I can't imagine not becoming physically ill at all.
At my ripe old age, neither of these activities will cross my future landscape. However, if you're looking for a non-experienced recommendation, trust me, sky diving seems to be the way to go.
Unless the chute doesn't open, but that's another story…