Would the 20" HB be better for a scoped AR over the lighter Government profile barrel? Why?

Are you ever going to carry or shoulder fire it?  If yes, then leave the scope off (or get something really light) and get a govt bbl.  If you're always going to be firing prone or off a bendh or bipod or some other rest, then get the heavy bbl, because it's heavier, (less movement of the gun), and won't heat up as much and will withstand sustained fire better (not as if you'd probably ever fire it enough to blow it out anyway.), and may be more accurate if you free-float it.  If you plan on doing a  little of both, they you'll have to either compromise on something or buy 2 of them!

I have a M4A3, and I'm getting a 20" A2 Govt.
I'm thinking about setting a 20" A3 up with scope and bipod, just to have something different. I love ARs.