Might want to check and see how far behind you are in upgrades. Even though the on-prem version will never have feature parity (new features hit cloud first) it could be that whoever runs your instance hasn't upgraded in a little while.
Feature parity is not really a goal of these products - they are totally separate teams, technologies and languages. If one team develops something awesome then of course the other will try to reimplement, but it's not really the case that features "hit cloud first".
You're saying the BitBucket cloud and server teams are using totally separate technologies and languages? That's not the impression I've gotten at all at every atlassian conference I've been to. Seems wasteful but nothing surprises me anymore.
Can confirm. The enterprise (aka Bitbucket Server) version gives you a two pane layout, with files on the left and changes to those files on the right.
Bitbucket Server (formerly Stash) is a completely different codebase from Bitbucket Cloud. They share zero code. One is written in Java, the other in Python. It's a constant source of confusion. The naming is because of a terrible marketing decision. Atlassian marketing does all kinds of weird things, like advertising Bitbucket as only supporting git despite also supporting mercurial.