Neck thickness does, indeed, change.
I have formed
many cases/cartridges. A short list of examples/results:
.22 Hornet to .270 REN = thin neck.
.30-06 to .35 Whelen = thin neck.
.280 Rem to .35 Whelen = even thinner neck (though, sadly, exactly the same as factory brass - due to the drawing process R-P uses).
.308 Win to .243 Win = thick neck.
.308 Win to .22-250 = even thicker neck.
.303 British to .22 Short Krag II = thick neck.
...and the list goes on.
When forming .35 Whelen from .30-06, the starting neck thickness is generally 0.018-0.019". Once expanded to .35 caliber, the neck thickness will generally be 0.015-0.016". That neck most definitely got thinner, unless you're suggesting my calipers magically change their zero for every post-forming measurement.
I DO get a longer neck, as well; but that's because I iron out part of the shoulder, and
turn it into part of the neck.
As for the original question-
Necking up results in thinner necks. If you're seeking sub-MoA accuracy at Creedmore, or need extreme neck tension, it's not for you. For most applications, it doesn't matter. -The farther you neck up, the thinner the neck will be.
Necking down results in thicker necks. You may encounter high neck tension (much more than desired), and difficulty chambering the cases/cartridges. How much this matters depends on the application, and the chamber in your rifle. Sometimes, you'll have to inside-ream or outside-turn the necks; sometimes, you won't. -The farther you neck down, the thicker the neck will be.
In the example provided here... if both types of available cases (.260 and .308) were of equal demand and value; I would neck up. Neck thickness will change only very slightly, from ~.260-.261" inside diameter to ~.280-.281" inside diameter. If you use digital calipers, accurate to only 0.001"... you may not even see a change.
However....
There is an additional complication to be aware of: The top of the shoulder of bottleneck rifle brass usually has a "donut" of brass around it. That donut gets relocated into the base of the neck of the newly formed (necked up) cartridge, and must be reamed out if it is detected at all. If you don't remove the donut, you can run into really funky bullet run-out, gas sealing, and sizing issues (especially with dies where a mandrel is used inside the neck sizing collet).
Best answer for a commonly available cartridge: Just buy the correct brass.