I haven't delved into 6.5-300 yet. I have shot my way through several 264win barrels over the years. Barrels are a perishable asset, just like the tires on your car. How you treat it decides how long it serves you. You need to decide how you want to drive it, and then make a decision on if that level of longevity meets your criteria. 6.5-300, and 264 win, are a crappy cartridge to practice with, but both do some pretty **** cool stuff a few times a year for the rest of your hunting career when you get them out of the case to verify them and hunt at whatever range you deem as ethical.
I use 1MOA as my standard of acceptable accuracy, when the rifle won't deliver that any longer it's time for the next barrel to go on. There has been barrels that I drove very hard, shooting five shot strings with as little time between shots as I could possibly have, and expect to hit my target. Most of those barrels fell below 1MOA between 400 and 500 rounds, one factory barrel only made 300, barely.
The barrels that I NEVER shoot more than twice and then allow them to cool completely usually make between 1,000 and 1,200 before they go south and that takes the better part of a decade to get to.
With the substantial increase in powder volume the 6.5-300 has over the 264win you could probably toast a barrel in 300 rounds pretty easy, if you wanted to. Treat it well and practice with another gun and it will last in terms of decades. You don't buy a Ferrari to park it and look at it.