if you are moving all of your users (and sites and not switching servers) there isn’t anything I can recall.
If user accounts change then relative addresses inside php will not work until you fix them all
If you have set any cronjobs to backup database, take a look into them again after the move
If there are folders outside the domain folder (those inaccessible through http request) and if you chose to move only few domains from an user then you might have to copy those folders as well.
VPS has worked smoothly, don’t remember any pitfalls, oh BTW keep a copy of DB FTP files for safety, if there is an option (when you are asked while setting up the vps) to keep the shared hosting along with VPS keep it (you will have to pay for both anyway) so that all files remain there as well