/vz and /home/vz will have similar contents, given that one is symlinked to the other. I don't understand why they aren't using the same space. No idea what /home/vps is.
Each container can have its filesystems in a different place. Suggest you look through the /etc/vz/conf/VEID.conf files and see where containers' files really are. Mine look like this:
VE_ROOT="/vz/root/$VEID"
VE_PRIVATE="/vz/private/$VEID"
Hopefully that will tell you what's actually being used.
I only back up the private tree on my CTs.. the root tree seems to be a working copy that disappears when the container is stopped. So far seems ok.