I personally have never seen significant differences in fluted vs nonfluted, but just to play devil's advocate:
Lilja - "If the barrel is fluted a maximum heavy varmint blank is usually used and for good reason. As we saw above, the larger the diameter, the stiffer it is going to be. Using a heavy varmint blank then gives us the maximum diameter allowed. Fluting a barrel removes weight, up to one pound or so depending on flute size. It also lowers a barrel’s moment of inertia value but not by very much. Some have the mistaken idea that fluting alone increases the stiffness of a barrel. This is not true. The fluted barrel of a given weight and length will be stiffer than an unfluted barrel of the same weight. The fluted barrel will not be stiffer than the same taper and length barrel that is not fluted though."
Shilen -
"What about "fluting" a barrel?
Fluting is a service we neither offer nor recommend. If you have a Shilen barrel fluted, the warranty is void. Fluting a barrel can induce unrecoverable stresses that will encourage warping when heated and can also swell the bore dimensions, causing loose spots in the bore. A solid (un-fluted) barrel is more rigid than a fluted barrel of equal diameter. A fluted barrel is more rigid than a solid barrel of equal weight. All rifle barrels flex when fired. Accuracy requires that they simply flex the same and return the same each time they are fired, hence the requirement for a pillar bedded action and free floating barrel. The unrecoverable stresses that fluting can induce will cause the barrel to flex differently or not return from the flexing without cooling down a major amount. This is usually longer than a shooter has to wait for the next shot. The claim of the flutes helping to wick heat away faster is true, but the benefit of the flutes is not recognizable in this regard until the barrel is already too hot"
I think really the take-away is that, like almost everything with shooting, every one has their own opinions.