Generally a heavy barrel will be more accurate for longer shot strings before starting to heat up and move around
It won't necessarily be more accurate than a light profile for the first few shots
The extra weight reduces recoil, and often helps hold the rifle steady
If you plan to carry it a lot, the light barrel will probably be better
If you intend to hunt in ways that don't require you to carry the gun as much, or you just want it for target shooting, then heavy would be the way to go.
If you can handle them both before you buy, it will be easier to decide, since the balance will be quite different