I'm not sure how a folder-compare app will generate particularly useful results. Albums are database entries, not files or folders.
I just played a bit with the test library I created back when I first got my hands on Photos - created new albums, changed the contents of other albums, and the only files or folders that changed were the five files contained in the Database folder. Even the files contained in the Albums folder did not change - no new files added, no files modified. It turns out the Albums folder only exists because my test album was converted from an Aperture library - a newly-created Photos library doesn't have an Albums folder at all.
No suggestions on how to open two libraries side by side - it's clearly not something Apple intends end users to do.
A folder compare will show whatever differences exist in the Masters, Previews, and Thumbnails folders - but that can be a very tedious way of learning why an album is empty - you'd have to know what images were supposed to be in that album in the first place.
Most likely, the albums are empty because the images were intentionally removed from that album, or were deleted from the database using the regular Photos delete function. If, for example, the Master image had been damaged or deleted/moved using Finder, the Preview and/or Thumbnails would likely still exist - you'd see the preview or thumbnail in the album, but might only run into an error if you tried to edit and the master can't be found.
