I looked at some loads that seem suitable for a decent sized whitetail. This is just a quick comparison from my Speer #13 manual to get a ballpark idea of powder use. I chose RE 19 to compare because all three rounds because all have data listed for this powder, so it's as close as I can get to an apples-to-apples comparison.
.243 Winchester
- 100 grain BTSP with a max load of 39.0 grains = 179 rounds to a pound of powder
.260 Remington
- 145 grain SP with a max load of 45.5 = 153 rounds per a pound of powder
.308 Winchester
- 150 grain BTSP with a max load of 49.0 grains = 142 rounds per pound of powder
I can't say how this will translate with bullets. Logic would suggest that a lighter bullet using less lead and copper will cost less to buy and less to have shipped to you. This may or may not be borne out at the counter of your favorite gun store. But at least with the .243, you're getting about two extra boxes of loaded ammo per pound of powder over the .308. For the seven pounds of powder you need to load 1,000 rounds of .308, you'll shoot 1,256 rounds of .243.
It's not a perfect comparison, but if you're shooting a lot, that could add up. Especially when you consider that you have less recoil from the lighter round (meaning more enjoyable shooting) and end up with just as much venison on the table and maybe even more accurate shooting from the extra practice and lighter recoil.
You're right that the .260 seems close enough that it probably doesn't matter though. You'd have to shoot about 2,000 rounds with the above charges to use a pound more of powder with the .308 than with the .260. The .243 will also probably be harder on barrels. You might wear a competition rifle barrel out sooner with it, so that's a cost to add in.
But it does use less powder.