ownCloud and Nextcloud are essentially the same for now. Up to about to about ownCloud 9.0 mainly because they share the same code base and history. With ownCloud 9, users can access both for the next two year, since the end of life ownCloud 9 is 18 months. After that users will need to decide which one to take. It is a fork on the road after all.
What will be the difference between projects?
According to ownCloud forums:
ownCloud GmbH focuses on the file sharing feature. The community provides additional apps (calendar, contacts, bookmarks, news). However, the company’s developers helped to build some of the apps (calendar, contacts). The enterprise version contains a number of exclusive features that are not available in the community version (Shibboleth authentication, File Drop, File Firewall, Auto-Tagging).
Nextcloud doesn’t exclusively focus on file sharing, they also provide support for apps such as the popular calendar, contacts app, and a communication platform (Spreed.ME). There won’t be enterprise-only apps. Enterprise users will benefit from professional support.