Having shot with URSA for the last two years at ranges out to 2,600 yards I'll be the first to say that there's a lot more to long range shooting than just the numbers. A rifle might look much better on paper but that's no guarantee it will work better in actual use. I knew a guy that used to absolutely dominate at 2,000 yards in competition with a plane jane 300 WinMag and another newbie shooter that got the high score his first match using a 7mm RemMag. That's against 50 cals, 375 Cheytacs, 338 Lapuas and even 338 Snipetacs. The other guns had much better stats on paper, but they got crushed by one very dialed in shooter with a smaller rifle.
Now, when the second stage came and we moved back to 2,600 yards he got absolutely flattened. But at the 2,000 yard line the "smaller" calibers seemed to dominate. Heck, I even took my 308 Winchester to the 2k yard line twice and I scored 1/10 and 2/10 respectively on a 36" steel target. There was one particular fellow that had been trash talking all day and almost had an aneurysm when I finally connected with the gong.
Of course, now they're all building insane super magnums like 375-50 BMG improved and 10mm-50 BMG. One guy even has a 50-20mm which from what I've heard will really clear the sinuses
But as for a point and click hunting round it boils down to what YOU can shoot well and YOU can afford to practice with. Larger magnums may not have more raw mechanical accuracy, but they do reduce the damage from a poor wind read or slightly wrong range estimation. You have to find what is a suitable envelope for accuracy and then work backwards from that to see what cartridge will give you enough of a safety net to stay within that envelope taking into account your own skills and abilities.
A word of warning, the further out you shoot the more little things can completely ruin your day. Case and point, one day I saw that my ammo box was in the sun so I tossed a towel over it until I was ready to shoot in the competition. That slight difference in temperature from direct sunlight vs covered was enough to completely miss the target.