What breaker size for box containing two GFCI circuits?
The breaker feeding the sub-panel must be sized not exceed the rating of the sub-panel. So, if you install a 60 amp sub panel you can't protect it (fuse it) any higher than 60 amps. Ditto for 100 amps.

The conductors should be sized large enough to carry the load of the sub-panel and be protected by whatever breaker they are attached to.