Mark,
the 260 Rem, 6.5X47L, and 6.5mm Hornady Creedmoor all give similar performance and barrel life (2,000 - 3,000 rounds depending on loads, pressures and firing rates). They're all capable of similar (very high) precision in a good quality rifle.
Pros and cons are:
Lapua brass (and brass by almost everybody else) for the 260. Lapua only for 6.5X47 and Hornady only for Creedmoor. Creedmoor brass can be reformed from 22-250 Rem allowing Lapua / Norma to be used, but it produces a slightly short case.
260 + Creedmoor use LR primer, so fewer worries about primer cratering / piercing with high pressure loads and a slack firing pin fit. 6.5X47L uses small primers, probably marginally better for ES and precision, but can cause problems with some stock factory actions.
260 sees heavier bullets seated very deep if the standard 2.800 COAL is retained either due to action length or need for magazine feed. This reduces powder capacity and charge weight. The other two use shorter cases and can use 140gn class bullets seated closer to the optimal position with a 2.8-3.00" COAL.
So, overall it's six of one, half dozen of the other as we say in Britain. My personal view is that this trio is ideally suited to 120-130gn bullets, but their BCs are such that they still work well at long ranges.
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Moving up a step, size and performance-wise, you have 6.5X55mm, 6.5X55AI and 6.5-284 in a rising order. I'm very fond of 6.5X55 as a really good performer in itself and a sensible compromise for size and performance between the 260 Rem class and 6.5-284 cartridges. All have a good range of quality made brass available including Lapua and Norma.
All need long actions to handle 139-142s seated optimally, although many short actions work fine for single-shot target work if you don't mind removing the bolt to eject a live round. (I do this with 6.5X55 in a Savage 12 PTA action.)
The AI is regarded by many as the ballistically optimal 6.5 as the case capacity is such you have a 100% fill-ratio with most suitable powders + 140s, and it's one of those design where Ackley-ising the basic case does make a worthwhile difference. The biggest problem in the past with this was dies availability, needing either custom made models or the sleeves in standard 6.5X55 Redding Competition die sets machined to the new case profile. I've got this vague feeling that Redding now offers the AI version in its Competition die lineup - but not according to the company's website.
All three are ideally suited to the 139-142gn long-range bullets and are proven performers in the right kit. It's a simple trade-off of MV v barrel life. 6.5-284 has more case capacity than needed with most powders - you have to use the really slow burners like H1000 and Retumbo to fill the case. With a 30-inch barrel, 6.5X55 will easily achieve the 2,800-2,850 fps MV level that seems to suit many 140gn 6.5mm bullets, and can go up to 2,900 fps or more. 6.5-284 takes you easily into the 2,950-3,000 fps bracket and some people run a fair bit faster than that. The downside is a big reduction in barrel life, so a fair few shooters try and find an accuracy node on 2,900 fps plus or minus 25 or 30 fps. Even so, most 6.5-284 barrels are toast at 1,200-1,500 rounds and it can be a mere 800 if you load the cartridge to its limits.
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The alternative to the 6.5mm sextet is .284 Win. Great accuracy, good brass (necked-up 6.5-284 Norma and Lapua), better external ballistics than any 6.5 if 175/180gn bullets are used, and a 2,000 round barrel life if loads are kept sensible. The downside is a bit more recoil.
I'd suggest you look at the cartridge guides listed on the main homepage to get a feel for the loads and ballistics. My own gut feeling is to choose one of the smaller trio allied to lighter bullets if you really want a 6.5 ......... or take the jump up to 284 Win for the next step up in external ballistics capability - a purely personal opinion and open to challenge from satisfied 6.5-284 owners.