there is a difference between copying a subtree of a TYPO3 instance into another TYPO3 instance (same version!) and updating a TYPO3 instance to a newer version (on another server). And mixing it would be even more complicated.
for moving a subtree the best idea is export/import (if possible, as there are some restrictions about the size. maybe split into smaller chunks)
For updating copy the whole system (Database, folderes AND TYPO3 version) to the new server, then do an update of the TYPO3 version there, which includes data migration and adaption.
If you need only a subtree with a new version: make a copy, reduce the database to the desired subtree (keep neccesary records and folders containing page configuration!). then provide the update.