I think the .308's great, and have recently reintroduced it (a Savage 11VT with Choate Tactical stock, Harris-style Bipod, and Mueller 8-32x44 target dot scope) into my shooting lineup. Will shoot mine for the first time tomorrow, Lord willin' and the creek don't rise...Testing an initial load with 178 ELD-X bullets and 42.2gr of IMR-4064. The .308 can make the 1000yd run, but it can also get a little winded when it's pulling up to the finish lone.
My main LR gun has been a 28" .260 Rem built on a 2001 Savage 10FP action. It will also test new 143gr ELD-X loads with 43.5gr of H-4350. This will be the debut of its Mueller 8-32x44 target dot scope. With the right BC bullet and at a higher altitude (I'm up at around 4500ft ASL), it can remain supersonic well past 1000yd.
My Savage 11VT .223 is good at 600yd with HDY 75gr HPBT-Match bullet and 24.4gr of Varget, and is my primary practice rifle as well. It has carried the Mueller 8-32x44 target dot scope for years of 300yd club matches. It resolves 22 caliber holes for me at that distance.
Tomorrow's test shoot will round out with a Savage Axis II 30-06 that has the Bushnell 4-12x40 hunting scope that comes as part of the 11VT package gun deal. It will test a 50.0gr IMR-4064, 178 ELD-X load.
These are my chosen chamberings. I am not personally familiar with the 6 and 6.5CM. The 6.5CM is an about equally good chambering compared to the .260, and has some advantage with loading longer bullets to magazine length than the .260, which has the alternative advantage of some additional case capacity. I see the 6CM as a reasonable alternative to the .243. At one time, the 6.5CM had an advantage over the 260 in factory ammunition availability, but that gap is closing.
For many, the .223 is the practice chambering of choice; that is most definitely the case for me, and I have successfully shot my 11VT at 600 in National MR F T/R competition just earlier this year. The rifle is a lot more competitive than I am at my advanced age and decrepitude. As a beginner comp rifle, the Savage 11VT is a good choice for F/TR in .223 and .308. A barrel replacement can turn the 11VT 308 into a 260 LR F-Open rifle.
There are a solid number of folks who will advocate an all out custom rifle for competition, and they are definitely right about that for shooters who have already weathered their formative competitive years. For me and those like me, a lot of that custom-built advantage gets nullified by the typical learner mistakes. I think the 11VT is simple, robust, and dependable enough to tide the beginner over until those improved skills can more responsibly justify much better equipment. My 11VT's are upgraded with the Choate Tactical stock
The 10FP custom has a factory pillar bedded McMillan A3 tactical stock that was one of several furnished at no cost by Kelly McMillan back around 2002 for inclusion in the SH .260 Rem Ghost Dancer project. I can never say enough good things about Kelly and those McMillan stocks.
I personally recommend the Mueller 8-32x44 Target Dot side focus 30mm scope. It's not a Nightforce, or a Vortex, but it's not junk, either. If the savings involved (they go for about $250-260 or so each) can get a shooter on the line sooner, and maybe with that savings invested into a startup handloading setup, it has already more than paid its way.
That's an opinion, but it's mine, so I favor it pretty solidly.
Greg