i love both bags. they look very similar, yet both stayed true to their own brands' styles. of course, i'm partial to the classic box because that is the bag i ended up investing in. the reason i picked the classic box is because the versatility of the strap. it can be adjusted long to be worn cross body, or shorter for shoulder carry, or removed all together and be worn as a clutch. whereas (from what i remembered) the chyc's strap is only available as the shoulder length. not to mention, i like the feel of the celine classic box leather better than the ysl chyc. however, the chyc's price does seem like a bargain compare to the classic box, which is a big plus.
they're both beautiful bags. you can't go wrong with either. please keep us updated on your decision!