A heavy barrel is stiffer than a light barrel, and has a greater mass to soak up heat.
The fluted barrel is as stiff (or nearly as stiff) and a heavy barrel, and is lighter to carry. SOME folks believe that the greater surface area created by fluting makes for better heat dissipation, but I feel this is minimal.
Which one? What floats yer boat. I have one .308 with a barrel thinner than a buggy whip. 3 rapid shots, too hot to touch. It is on a very Little carbine made for a deer hunter- you are gonna CARRY that rifle a lot, and fire a couple of shots.
But I have a .220 Swift with a barrel that could be used as a truck axle. Heavier than a mortgage. Prairie dog gun. Not going to be carrying other than from the truck to where I am setting up. Going to shoot it until I run out of ammo, Pdogs, or daylight.
(Jon- I have to learn to type faster!)