I've seen a lot of discussion on this topic in radio-controlled plane groups, and I've been working out winglet design on the r/c planes I've built for years. I've also seen the results of tests done by laboratories. (on the internet somewhere, hunt & I'm sure you'll find them) I think it's pretty well established that upwards is better, though a small projection on the bottom seems to be a good thing.
The way the tip transitions into the winglet is probably just as important as the shape of the winglet itself. I've had several flying wings that flew well without winglets or any vertical surfaces at all, by shaping the tips. The stock wings, with squared-off tips, don't fly well at all without the winglets.
Of course, if someone can provide evidence of an advantage for downward-pointing tips (other than non-aeronautical reasons such as LG convenience, such as on the Quickie) I'd like to see it.