Hmm..well, barrels are made differently for a host of different reasons. Leaving "flutes" out of it for a moment, heavy barrels are felt to be more rigid/stable when shooting with a rest...and having more mass, can be very slow to heat up. Less vibration, etc. All considered good things from an accuracy POV. Favored by target shooters, varmint hunters..any time you anticipate a high-volume of shooting, and a stationary shooting position WHILE shooting. They tend to be too muzzle heavy for off-hand/unsupported shots.
Flutes (straight) achieve a few things. They allow a barrel to be a larger diameter and cash-in on the rigidity that brings, yet with material milled away...weight is reduced and there is a greater surface area to dissipate heat more quickly. So...some of the benefits of a heavy barrel, with less heft/carry weight. Spiral flutes (if that's what you're asking about, not the appearance of some hammer-forged barrels?) achieve, I think, some of what deep...straight flutes do depending on how many/how deep, but seem to be more of an aesthetic consideration.
There seems to have always been some debate (when it comes to 22LR) about whether or not heavy barrels make any difference because quite frankly, there isn't enough powder burning in a 22LR round TO generate much heat. Especially in the land of 5-10 round magazines.

Even more the case with bolt guns~you just can't fire them fast enough! However, having owned lots of standard-weight AND heavy barrel rimfires, I FAR prefer heavy barrels unless it's a rifle I'm carrying long distances..and shooting very few shots with. I might also add, most of the spiral flutes I've seen on rimfire barrels are so shallow that they are likely nothing more than an aesthetic treatment. Centerfire rifle barrels (where heat DOES become an issue quickly) tend to have real fluted barrels, with deeply-milled slots to do what they're actually meant to do.
My opinions only...