I don't have either yet, but I've seen them in the stores IRL, and I really prefer the Box. The Twiggy is so slouchy and sags in the middle...
I think perhaps a better comparison would be a Box against a Mini-Twiggy, as they are reaaaaally similar sizes and apparently, they hold pretty much the same amount of things. However, I haven't seen a Mini-Twiggy IRL before, so I can't choose! =)