First one should ask though: why? My main motivation was that many of the apps I use were easily available in the nextcloud store, while with owncloud I had to manually pull them from github.
Additionally some of the app authors migrated to nextcloud and did not provide further updates for owncloud.

Another reason is this:

the graphs above show the number of commits for owncloud and nextcloud. Owncloud has taken a very noticeable hit here after the fork – even though they deny it.

From the user perspective the lack of contribution is visible for instance in the admin interface where with nextcloud you get a nice log browser and system stats while with owncloud you do not. Furthermore the nextcloud android app handles Auto-Upload much better and generally seems more polished – I think one can expect nextcloud to advance faster in general.

Migrating

For migrating you can follow the excellent instructions of Jos Poortvliet.

In my case owncloud 9.1 was installed on Ubuntu in /var/www/owncloud and I put nextcloud 11 to /var/www/nextcloud. Then the following steps had to be applied:

1. put owncloud in maintenance mode

   sudo -u www-data php occ maintenance:mode --on

2. copy over the config.php

   cp /var/www/owncloud/config/config.php /var/www/nextcloud/config/

3. adapt the path in config.php

   # from 
   'path' => '/var/www/owncloud/apps',
   # to
   'path' => '/var/www/nextcloud/apps',

4. adapt the path in crontab

   sudo crontab -u www-data -e

5. adapt the paths in the apache config
6. run the upgrade script which takes care of the actual migration. Then disable the maintanance mode.

   sudo -u www-data php occ upgrade
   sudo -u www-data php occ maintenance:mode --off

and thats it.