Place a good bullet from any of the 3, and they work. For simplicity and factory ammo, if he will not handload, a 270 like the older parent 30 version, is never a bad choice.
The first rifle I wanted was a 270, but had to settle for a 7RM, later a 243, and so many since. I have used 3 270s to good effect. Never left me wanting....
Give me a 140 Accubond or 150 Partition and I will happily hunt anything in NA, non-dangerous. Same for a like-loaded Creemoor or 7/08
The 6.5 is popular for many reasons: Great accuracy, low cost quality ammo, light recoil, and deadly results, all in factory rifles.
Better? Subjective perhaps. Those qualities above might be better for some, for others, same-same. Relative to the shooter.
For a hunting rifle that will also be used on a lot of paper and steel, recoil will be a consideration, nod going to the 6.5
I'd consider the ammo question, will one handload or likely just buy factory. No doubt the 270 has the longest track record but I doubt the other 2 will ever be obsolete.
