My opinion is solely based on moose, black bears, grizzly bears, mountain goats, dall sheep, and caribou NOT elk so take it for what its worth. I have seen animals killed with 243, 7-08, and 308. Not 260 yet but my wife has one and we hope to get to use it on an animal at some point. That said if I was buying a rifle for a growing hunter with the idea of an elk rifle it would be 7-08 or .308. Reason being you can load them down with 120TTSX (7-08) or 130 TTSX (.308) for the recoil shy and still have them going at or above 3K fps for a realatively flat shooting round. At 300 and even to 400 yards the "lousy" BC of a 130 TTSX isn't much to "worry" about IMO. A 260 140 accubond at 2850 with a BC of .509 compared to a 130 TTSX at @ 3050 (what I get out of my 20" barrel .308) is only .5" difference of elevation difference (in favor of the 130 TTSX) and the 130 TTSX drifts 4" more than wind drift at 400 yards. And in a 10 MPH wind you likely aren't going to be shooting elk with at 400 anyways. At 300 yards the difference is only 2".
But what the 308 gives you that the 260 doesn't is the ability as the shooter gets older to use the same rifle with significantly heavier bullets. Eventually you will could be using 165 to 180 Accubonds at 2800 to 2650 fps. That is more lead than a 260 will ever be able to shoot. Not saying the 260 is a bad choice, but I believe the 308 gives one more options especially when ranges are limited to 300-400 like you say. At those ranges the lighter bullets of the .308 or 7-08 with the not as "cool" BCs are a non-factor in my opinion.
I think folks get wrapped up (myself at time fall into it as well) too much with the bullets BC and SD. Placement is everything. I just don't see a reason to limit yourself with a 260 that can only shoot 100 to 140 ish (yes I know they make 160s but I'm not advocating loading 220s in the 308 either

)grain bullets. Options are a good thing and the ability to load up different loads as the person grows is a great option. At the end of the day they all work, so why not choose the one that gives the most options. Sounds like you aren't trying ot setup a LR rig but a youth rifle so don't worry about BC.