When it comes to "which is best" there is pros and cons over cut vs. button rifled. Cut rifled barrels is the old methold, been around since muzzle loading times, button rifing is newer and does form all lands and grooves at the same time vs. one land at a time with cut rifled barrels. This helps to speed up the barrel making. some experts say that using a mandrel with the button rifle barrel, lends to a smoother finish on the barrel interior,they say the same for hammer forging, and cut rifling has a tendency to leave more tool marks from the cutter. but lapping a barrel can leave it as smooth as one that was button rifled.
I use mostly Shilen barrels and have had very good luck with them. I think it is more important to go with a brand that has made a name for itself in achieving very good accuracy. This is more important,IMHO, then how the barrel was rifled. Stress relieve of the barrel, total accuracy of the lands & grooves for the intire lenght of the barrel also play a very important part in the final accuracy. I prefer Shilen, due to getting very good accuracy at a reasonable price, but there is other makers out there that can deliver on a very accurate barrel.
Bottom line, for a hunting rifle, you do not need a barrel that was made for bench rest shooting and .150 ten shot groups, but if money is no object, go with the best and be happy, but even the benchrest crowd can not all agree on who makes the best barrel.
Also you need a good gunsmith to put it together, a poor assembly procedure can screw up the best barrel in the world.
RELH