Random would be even more unique. The solution (to this particular problem) is for a majority of users to set the exact same headers, regardless of the reality

Some browser vendors have started to remove the specific version from the User Agent string, for instance. Tor browser window is an actual square specifically to make that value (browser width & height) the same across all its users and improve their privacy (by making that value useless in finding uniqueness)

Hope that makes sense, sorry if I mis-explained some things