Well, that kind of depends on what you're looking to do with the rifle. If you're building a hunting rifle that will be used for long-distance tracking and stalking, a thin barrel is going to be lighter and easier on you to carry. But a quality light-profile barrel in a well-built and well-bedded rifle will be quite likely to give you more accuracy than you need for even fairly long hunting shots. If you find a load it likes and learn your cartridge's trajectory and learn to estimate range well (or get a good rangefinder), the rifle will be likely more accurate inherently than you're able to take advantage of under field conditions and at the more limited ranges you'd be ethically shooting at game animals. In such a situation you might choose a long barrel to keep the velocity up, thus making the trajectory a hair flatter so the gun is more forgiving to range estimation errors -- but the light profile makes the gun more agreeable to carry for miles.
If you're building a long-range target gun to shoot small groups and/or compete with, you likely want to make the barrel as heavy-walled (and therefore, stiff) as the competition rules allow. In those cases, accuracy is paramount above portability, as you only have to carry the thing from the trunk of your car out to the firing line. And matches will be won by very small margins of accuracy. Some folks contend that fluting stiffens the barrel even more than simply making it a heavier profile, but that's hotly contested. Almost anything else done to artificially stiffen the barrel is getting into crazy experimental stuff that isn't likely to be a good return on the investment.
In the end -- in either case -- there's a great deal of debate among hunters and target shooters about what is optimal, and no two barrels are perfectly equal anyway, so a great barrel in a great rifle may outshoot any number of shorter, stiffer, thicker, (whatever-er) barrels which should, on paper, beat it.
That's what makes all of this so much fun -- there's no perfect one way to do it, and in the end, shooter skill is the final (very) wild card that can make an average barrel look great, or a great barrel look like a dud.