|Ok, TeamViewer reduces the colours, cuts some other details for displaying the screen, depending on the quality and speed of the connection.|
VPN tunnel itself needs a portion of speed for itself, for tunneling and encryption.
The rest of the speed can be used by Remote Desktop.
I prefere RealVNC for such things.
The commercial version supports encryption, works fast and reliable.
The display quality also depends on the quality and speed of the connection.
But all in all, you get a much better quality on your screen than with TeamViewer.
Disadvantage of RealVNC:
When the remote computer works on dynamic public ip address, you need services like No-IP or DynDNS, to be able to access the remote computer.
TeamViewer works with central servers, where the TeamViewerQS program transmits the current public ip address to such servers, so that one gets the current ip address of that machine from this servers. So no No-IP or DynDNS is needed.