Migrating to a new PC.

Not sure if it's the same for GOG version, but retail version saves in:
C:\Users\<user name>\Documents\My Games\Ironclad Games\Sins of a Solar Empire <version name>\
With one folder each for Save-MultiPlayer and Save-SinglePlayer.
All your maps from galaxy forge and designer are in here as well, along with settings, recordings, and mods all in thier own folders.

Can't think of a reason why it would be any different...