I have four machines running Windows 10 Pro, all upgraded from Windows 8.1. I use mstsc to remote between them. When I do this several things commonly go wrong.
The first workflow
1a) On first connection attempt it shows the remote machine login screen, but it freezes. You have to disconnect, it never unfreezes.
1b) You reconnect and get a message saying "The Remote desktop services is currently busy". You have to disconnect.
1c) After trying to reconnect and getting the same message you eventually get granted access and it will start working correctly.
The second workflow goes:
2a) On first connection attempt it freezes showing the login screen. Forcing you to disconnect.
2b) You reconnect and this time it gets as far as the desktop, but it is still frozen and you have to disconnect.
2c) The third time you reconnect everything appears to work fine.
Which machine I use doesn't affect success rate.