We have a productive GitLab 6.8.1 running. I've set up a parallel VM with GitLab 7.10.4. Now I want to move all data from the old installation to the new one. I've already found a way how to move the bare repositories, but I have no clue how to import the user account information, issues, etc.
EDIT: The thing is further complicated by the fact that the original installation was built from source, was running on Debian, used MySQL as a database and the whole installation was pretty much messed up. That's why I didn't manage to migrate the old server and decided to set up a new one. The new server is an Ubuntu machine with GitLab installed from apt-get package (I think that's Omnibus, but I'm not sure what this means.) The new installation seems to use PostgreSQL.
FYI You haven't specified whether the old or new server is running a source installation or omnibus, or whether you're running a MySQL or Postgres database. Instructions differ depending on these factors, so please clarify and I will update my answer.
The first thing is that you will need your old and new servers to be on the same version of GitLab. You cannot migrate anything other than repos without having synchronized versions.
Depending on your reply to the above you will either follow instructions similar to the backup and restore tasks or by running the backup and restore tasks. Both options generally require you to manually copy configuration files or migrate settings from multiple files to a single new file (in the case of going from a source install to Omnibus). The Omnibus upgrade guide above lists the configuration files that need to be migrated depending on your environment.
Update based on edited question: There's a guide specifically for that scenario in this section of the Omnibus upgrade guide, using Option 2. You still need to have the same version on both old and new servers, though, I believe.