Restore Time Machine backup from Mac Mini to Mac Pro?

Solution 1:

Yes, you can just use Migration Assistant to transfer your files from the old computer to the new. There's no need to create a Time Machine backup first in order to migrate data and settings.

It does not matter that one is a Mac Mini and the other is a Mac Pro.

Migration Assistant will be default allow you to transfer the data over the network. Both computers need to be on the same local network. It doesn't matter if it is a wired connection or a WiFi connection - however a wired connection is often fastest.

Solution 2:

Solved: I had to uninstall Mac Server from the Mac Mini!