I ordered from both not too long ago. I ordered two pairs of glasses and a pair of sunglasses from EyeBuyDirect, and just one pair of sunglasses from Zenni. Over all my Zenni experience was much better, because they processed and completed my order much quickly. But that could also be because I ordered 1 pair through them vs 3 pairs through EyeBuyDirect.
I also noticed that the two seem to have different styles of sunglasses. Zenni, on the average, seems to be cheaper. And I feel like my Zenni sunglasses are better quality than the EyeBuyDirect ones. But at about $15/pair, I'm not complaining either way. My advice would be to find a pair you like on either site and order them. If you don't mind spending the extra money, but both pairs, that way you have a back up pair in case the other breaks.