Start the nextcloud client once, and close it right when the wizard asks for the server etc
Copy you existing owncloud.cfg to the nextcloud.cfg created in by the client in step 3.
On Linux distributions:
On Microsoft Windows:
On MAC OS X:
Start the nextcloud client. It will ask for the password and afterwards pick up where your owncloud client finished -> no new data will be transferred.
edit: put in the default paths where the config files can be found.
This worked flawlessly for me. Just make sure that no client is running anymore before you do step 5.