Coin-ops is BP's brand name frontend (basically all in one emulation program)
Coin-ops is like base model
Premium is like the model with all the nice options aka ART
Both are a Coin-ops brand. Just think of a truck or car having an updated model is premium.
Coin-ops although is almost a completely different program than it's Premium version.
Coin-ops usually has a static image background with a in game video to demonstrate each game. The different filters year/name/times played/model/type and etc is what makes Coin-ops different than premium. It makes sitting through finding thousands upon thousands of games easy to manage.
Premium is very dynamic with several moving images on screen with each game. Premium is setup into something similar to a folder system. Each pack/game folder has whatever you want in each folder (assuming the frontend supports it).
The beautiful art is what truly sets this apart from Coin-ops. It's truly amazing the visuals that are possible from the old Xbox.
Premium since it runs on a folder style can have several different packs/folders with say for instance an NES pack and a Zelda pack both on the same build. Meaning you could have as many of the same game/ROM as you want in different packs/folders.
Coin-ops since it is based on organizing can only have one game name in the whole build. That way it can keep your build tidy and clean.
I have both on every Xbox I own. Both have their own special purposes. Boils down to how much room you have.
Have a good one bud hope this helps!