Well, as I have said, I'm not very familiar with Coppermine; in fact, I haven't seen a Coppermine site in years that I can recall. We do have a comprehensive list of our features:
Comprehensive Review of PhotoPost Options
which you can use to compare options. For years PhotoPost has innovated many features duplicated by other gallery products - our newest items include a user configurable layout option, and IPS (Image Protection System) which can be used to move original images out of the web directory and many other features that are unique to PhotoPost.
Maybe someone with more experience with Coppermine can chime in.