No personal experience with Tikka fluted barrels, but I've had standard Tikka's and have some experience with fluted barrels on other guns.
The standard Tikka's shoot about as well as anything out there, and are already the lightest gun you'll buy for under $1,000.
Flutes are a sort of compromise between light weight and stiffness. A heavy barrel will be the stiffest, and theoretically the most accurate. Standard Tikka barrels have a bit more meat in them than most guns coming close to their overall weight. Tikka reduces the weight in the action and stock. Other guns such as the Remington Mt rifle and Winchester Featherweight get most of the weight reduction from thinner profile barrels. The Tikka is still lighter, even with a heavier barrel.
If you flute a heavier barrel you can get the weight close to the Featherweight contour barrels, and still retain most of the stiffness. They won't be quite as light as the featherweight barrels, nor quite as stiff as before the fluting. But the flutes can help reduce weight by a few oz, without giving up any noticeable accuracy.
It is not just cosmetic. My Winchester 70 EW with a fluted barrel is exactly the same weight as my Featherweight although the EW barrel is much thicker. Accuracy is a bit better with the EW, especially after 2 or more shots are fired.
On some rifles it makes a lot of sense. I'm not sure I'd fool with it on a Tikka. They are already pretty light. It might make them just a bit too light. But that is personal preference, you'll just have to handle both side by side and see what feels best to you. If you want to save a few oz of weight, and it is worth the cost to you then there isn't much downside.