The difference between Gibson Les Pauls is normally cosmetics and electronics. Meaning, a Studio and a Standard are both going to have mahogany bodies and necks and maple tops and nitro-lacquer finishes, but the Studio is going to lack binding, might lack flame or at least AAA flame top (might be AA) and the neck/body tenion joint might be slightly different.
Standards are named such because they are the "standard" by which all other Les Pauls are judged, so to speak. Customs add more cosmetics (triple binding, 3 ply pickguard, different heastock inlay, etc...) and Classics usually use uncovered ceramic magnet humbuckers and lose the pickguard, but are similar to Standards in many other ways.
The compound radius neck is a cool feature and I've yet to play one.
side note: I wonder if the passing of Mr. Lester Polfus has lifted any former restrictions that he may have placed on the making of the guitars with his name on them? Gibson seems to be really stretching the LP in it's newest models as never before when Les was alive. Just wondering...
Every Epiphone that I know of is going to be made of similar materials, albeit probably sourced from cheaper suppliers, and will have polyurethane finishes. Poly is strong and shiny looking. That said, most of the major guitar manufacturers that I know of use lacquer finishes. Epiphones are nice, but they're no Gibson.
The various humbuckers use different magnets and wire to achieve different sounds and output levels. Differences are subtle, but they are there. I'm not up on every single Gibson humbucker, but I do like the Burstbucker 3/P-90 combo in my Les Paul BFG. P-90s are AWESOME pickups! The bite of a single w/ the warmth of a humbucker.