The biggest advantage of tip-down carry is that if the blade doesn't retain well in the handle and it opens up a bit in your pocket, you won't reach in and cut your fingers. This accidental-opening is generally only a problem with liner lock knives, and then only when the ball-detent system doesn't work well (which is fairly often, sigh. don't get me started on liner locks).
The disadvantage of tip-down carry is that there's just no way to pull out and position the knife without pinch-gripping at some point, something I'm not looking forward to do with sweaty hands under stress. With tip-up, you'll have 4 fingers curled around the clip on the outside, reach your thumb in your pocket and put it on/in the stud/hole, then withdraw; at no point in the entire opening motion do you need to pinch grip. As a result, it's not only more secure but it can be a hair faster. In addition, if the clip loosens up, it's easier for a tip-down knife to fall out of your pocket, because more of the weight is up high compared to tip-up.
Overall, I'd agree with Marvin that it's not as much of a big deal as people think. I like tip-up for its better security during opening, but only when I know the knife stays shut when it's supposed to. Regardless of where the knife is clipped, it's much more important to me that the clip be mounted as high as possible. That means ABOVE the pivot (not at the pivot) for tip-down knives.