I'm a fan of the .308, though I do concur that 6.5's are easier to shoot at longer ranges. Most of the comparisons you find between the .308 and 6.5's and 7mm's are usually showing the .308 using 168's at 2600 or 175's at that same speed. But if you look at some of the other bullets you might use in the .308, it can close the gap significantly...
A very interesting comparison is to consider the .308 pushing the 155 grain Lapua Scenar at 2850 fps (easily and safely done)... this brings it into the realm of wind drift and trajectory with sensibly driven 6.5's and 7mm's on the .308 parent case.
That said, I've shot the lighter bullets from my .308's at 1000+ yards and have found that the heavier bullets still seem to shoot more accurately--by a small margin anyway. This is likely because of the 10 twist of my Savage .308 barrels.
In my LE2B Savage (basically a McMillan stocked 10FP) I have actually gone to a 200 grain Matchking, pushed by 43 grains of Varget (a bit over max, but proven safe even in 95 degree weather in my rifle)... this load makes right on 2600 fps of MV, and hits significantly harder (about 25% harder) at 1000 yards than lighter .308's and non-magnum 6.5's.
Heavier bullets like the 200 SMK and Berger's 185 grain VLD's at around 2650 fps (Varget will do this easily) deliver a heck of a wallop at 1000 yards, compared to the smaller calibers.
So the .308 isn't dead--nor will it be for a long while. It's got lots of options, for those who want to "expand its horizons" so to speak.
For most of my shooting--even to 1000 yards--I enjoy the gentle recoil of 175's and 178's (Hornady) at around 2600 fps MV. It's true, you'll need to get a little better at calling the wind correctly with bullets which drift farther, but it can be done.
Here are some targets I've shot while testing various bullets at 1000+ yards from my Savage LE2B (McMillan stock, heavy 26" 10 twist barrel)...
The Nosler Ballistic Tips in 180 grain weight are good hunting bullets, but appear to have a lower BC than Nosler's published .500 number. These were dropping well below the point of aim, and a couple of them drifted left off this target...
Good vertical dispersion on this 175 SMK load means it's got a low velocity extreme spread... gusting winds took some of the shots off the board to the left, but this load in good wind conditions is a solid 1000 yard performer.
Only 3 of these 7 shots of Lapua Sceanar, 155 grain weight, stayed on the target board. The three shot group that did form is respectable, and I'd assume the other shots would have been vertically speaking with these three... but alas, the wind got them, so who really knows. :-)
another test load from one of my .308's at 1040 yards... this one was the Sierra 175 grain Matchking with 42.4 grains of IMR 4895, a favorite load recipe I use often.
So the .308 can certainly do a good job for you at long ranges...