My humbucker mounting rings are sloped - high side towards the bridge. I was thinking of replacing them for chrome ones - but the ones I have found are flat.
Is there a distinct advantage to one style or the other?
If they're on a LP, you want the slope. They're sloped to compensate for the neck angle. You can find chrome ring caps to go over the stock ones. They're really thin and just sit on top of your existing rings.
Exactly. Guitars with a TOM/Stop tailpiece need the neck angled to keep the strings down on the fingerboard, especially LP's with an arched top. If the top is flat, the angle will be less.