I would think better than bigger is more stable; instead of a conventional barge, they could use a semi-submersible or some other optimized hull form to ensure a more favorable motion response in a given sea area. I think I remember reading that they use a run-of-the-mill cargo barge, which is probably ideal for logistics compared to a highly specialized vessel.

I'd love to hear from naval archs or hydrodynamicists who are working on this (surely there are some).