I recently moved my personal project from GitHub to GitLab and the whole process took me less than a minute, with a simple git remote set-url on the client side.
The future is amazing.
Not wanting to diminish what GitLab is doing, but what you mention is an inherent characteristic of git itself that applies the same way to GitHub, Bitbucket and a self hosted git bare repository. Any git host should expose a git interface for it to work as a git repository.
Yes, but they simplified it a lot. I just connected to github, chose the repository and clicked import. Maybe all of those services have it that way, but I'm just glad that GitLab had it.
That is a different case than configuring a different remote on config and pushing to another host which is what I interpreted reading your comment, my bad.
Out of curiosity, does the import process include all issues, PR and comments?
Sure!
The only reason I wasn't using GitLab before is that I had a writer working remotely on my game and I didn't know how to explain to her how to use it. So I had moved everything to GitHub and told her to use their desktop app, which makes the clone/commit/push/pull flow amazingly simple.