With tip-up, you're grabbing the knife with the blade oriented upside-down, but with the handle positioned "right-side up" relative to your hand. So all you have to do is "right" the blade via the opening mechanism (thumstud, hole, etc.), which is conveniently located right where you placed your thumb when drawing the knife. So you have a full-grip on the knife through-out the draw as someone mentioned earlier, along with fewer movements in getting the knife into action (although with some knives you have to reposition your hand a bit).
My personal preference is tip-down, mostly because my first knives were tip-down, but also because with larger knives, it's easier to pull at the exposed portion of the handle and flip it into my palm rather than dig down into my pocket, especially if I'm carrying something else alongside the knife. In addition, when space is at a premium, and my knife is packed in tight, it's faster to get the knife out tip-down for me, rather than reposition my hand up the handle drawing tip-up, throughout which the knife is somewhat insecure in the hand. Incidentally, I can open an unfamiliar knife faster tip-down and usually can open my EDC faster tip-down as well under similar conditions when using the thumbstud/opening hole/etc.(although the security of grip of the tip-up to draw is nice at times).
Tip-down is generally safer, although I've never had any real problem with a knife opening in the pocket, as long as the edge is positioned at the seam (although this limits carrying options somewhat).