Yes, in your case there would be a lot of steps (all major versions) and your idea to make a new setup is probably the better solution.
Some carddav and caldav clients can make backup copies themselves, so you could use this, then connect to the new server and save the data back. There are also script to do this from outside:
Perhaps there are a few others.
Since you have different systems, you can set up the new setup and then just try different solutions 
I’d rather try a solution that uses caldav and carddav to copy the data instead of manually copy the ownCloud and Nextcloud database. There is a considerable version gap, there might be some things that have changed. There are probably a few more topics here on the forum.