The difference between them in a 30-inch barrel target rifle is around 100-150 fps MV with 140gn class bullets. Both give excellent precision in the right equipment.
IMO, the .260 (and its 6.5mm Hornady Creedmoor and 6.5X47mm Lapua ballistic contemporaries / competitors) are best suited to 120-130gn class bullets. They will handle 140s fine but rarely seem quite as comfortable and the calculated ballistics benefits are nil to modest. The 260 comfortably gives the 123gn Lapua Scenar 2,950 fps (many people run them at 3,000 fps with the small 6.5mm cartridge trio) and it's an amazing long-range performer for such a 'tiny' bullet - 1,417 fps retained MV at 1,000 yards with 7.6-MOA drift in a 10mph 90-deg crosswind. The 139gn Scenar at 2,800 fps, a similarly reasonable and attainable MV from 260 with a long barrel, also capable of being raised, is slightly slower at 1,000 yards with a marginal drift reduction. Yes, I know there are higher BC 6.5 140s available but their benefits over the 123gn Scenar (which appears to perform better on the range than any ballistics program predicts) don't seem to show up that much if at all.
That's my findings on the 260-class cartridges, but I'm sure many will disagree.
6.5X55mm in a modern action and with Lapua brass (Norma too I'd imagine, but I've no experience of using it) will safely run at the same sorts of pressures as .260 Rem Lapua case handloads and give identical life before primer pockets slacken. With a bigger case, more powder = more energy but at a lower efficiency in terms of muzzle energy produced per grain of powder and greater wear and tear on the barrel throat. My Savage 12 PTA with Bartlein 30-inch barrel rifle has got the 139gn Scenar almost to 3,000 fps, in fact it'll be over 3,000 as that was 2,999 fps average from an optical chronograph some feet ahead of the muzzle. This is a 'silly' load though as it was pushing the cartridge too far, beyond its ability to produce small groups, and almost certainly with a case life of only two or three loadings. That was with Viht N160, and a case-filling load of N165 produced superb precision (third-MOA groups) and 2,919 fps. With both of these powders being standard single-base, 'high energy' types - Viht N560 and the slower Alliant propellant grades - will likely provide a bit (50 fps?) more at the cost of yet higher barrel wear.
To my mind at any rate, the 6.5X55mm handles 140gn class bullets really well and the good choice of superb 139-142gn models available makes this bullet weight the obvious way to go. At ~2,900 fps MV, the cartridge becomes a truly competitive mid-range match round and viable 1,000 yard performer, although it'll always be at a disadvantage ballistically to the sevens starting with .284 Win sized models.
As is so often the case, it's a matter of balancing usage (discipline and distance), recoil, external ballistics, and barrel life. The 260 class trio will perform superbly at short to mid ranges with barely noticeable recoil in a heavy rested rifle; the 6.5X55mm loaded fully increases the viable competitive range and still offers great mid-range performance with very acceptable recoil making gun handling easy but probably knocks 40-50% off the 260's barrel life; 6.5-284 Norma loaded to the gills is still a great long-range number but gives only 900-1,200 rounds out of a barrel.
Before lots of hunter .260 Rem shooters put in posts telling me their rifles give fantastic performance with 140s, I'll add that I'm talking long-range slowfire target shooting here. Yes, the 260 is a very good perfomer on deer with 140gn bullets and that's likely the best bullet weight choice, although that's a guesstimate from my point of view since I don't 'hunt' (stalk deer we call it in GB). Likewise, the 260 and equivalents + 140s may be the best choice for Silhouette competitors - we're not allowed metallic Sillhouettes in the UK on 'health and safety' grounds despite the lack of reported accidents from those many countries that do shoot this discipline.
Since you're contemplating a 24-inch barrel factory rifle, the ballistic differences will be somewhat (heavily?) reduced. I'd probably go for .260 Rem in that scenario. 6.5X55 is a lovely cartridge to load and shoot with though, so it'd come down to tossing a coin on their respective abilities. On the other hand, if you're likely to sell the rifle within a few years, you have to consider that factor too. Over here in the UK, a 6.5X55mm factory job might actually sell a bit faster for a bit more (that reversed for custom short/mid range target / sniper / McQueens builds), but I'd imagine the 260 is better known and more desirable in the US?
