Feel to an individual shooter and/or hunter is the biggest difference. .17hmr barrels do warm up and effects can be seen on accuracy rather quickly. Heck, even a .22lr can warm up to the point of changes in the point of impact in just a few rounds. So yes, a heavy barrel might help if you're shooting multiple shots back to back to back. Also, as some have stated they like the extra weight and think it's more stable. It probably is but still that comes down to personal preference.
Frankly, there is not much if anything more inherently accurate to a bull barrel. All barrels have harmonics and sporter barrels, rimfire and centerfire, can display a great amount of accuracy and unless one is sitting over a prairie dog town or needs the extra weight to help them steady the gun than a sporter barrel is all you need.
BTW, seen consistent dime sized groups from the Savage .17hmr sporters. Buy with confidence.
LK