By some people, Apache2.0 is more free than GPL (any version) because it gives the freedom to make your code (and other's modifications to it) proprietary.
For others, GPL (any version) is more free than Apache2.0 because it guarantees that not only your code remains free, but also modifications that others make *must* be free.
So, if you are one of the latter guys (as FSF clearly is), AGPLv3 is more free than GPLv3, since modifications *must* be free even without a distribution of a binary, just because of a mere "utilization" even remotely through a web service.
On the other hand, if you are in the former camp, AGPLv3 is less free than GPLv3, because of the very same reason. But if you are in such a camp, you'd probably not use the GPL in the first place, so I think the issue of the v3-plus is moot.