All depends on what your intended use is. Plinking - makes no difference, hunting - go light, range only and competition - go heavy but consider what type of competition you are wanting to do - no fun hiking umpteen miles under a time limit with a heavy pack and the HMS Titanic for added weight; those are general rules but there are always exceptions. General advantages of heavier barrels are they heat slower, less heat reduces chance for possible POI shift and mirage which occurs if barrels heat to 165 F or above, it can also increase barrel life depending on barrel material, they also help mediate recoil through added weight and reduced recoil means more stability; however heavy barrels generally also mean heavy rifle and heavy rifle means less motivation to do long hikes. In some cases heavy barrel can also mean some stocks/chassis won't fit, or balance the right way because most of the weight is forward. All that said, the difference between a 5.5 and a 6 contour are not world shattering. Look at the total weight and decide what you can live with. Also consider the base, rings, and scope and possibly bipod, monopod, and assorted rails, or doodads you might want to hang from your rig; an ounce here and there can quickly add up to a boat anchor.