Copy home directory from one Mac to another both running macOS Catalina

Migration Assistant was designed by Apple to do just that. A direct copy may have problems because some of the things in ~/Library depend on MAC address, and some may change due to differences in hardware or O.S. version.

With 1.3 TB, speed cannot be expected.

You’ll have to have nothing else running (not even Time Machine or Spotlight indexing) to avoid error -42. According to http://www.macwizard.com/errors.html, that means “too many files open.” If no other apps are running, then report to Apple that Migration Assistant has a bug. Actually two of them—it should not open too many files, and if it does get that error, it should close some and keep going instead of quitting.