The .223 is easier to resize because you are moving less metal.
Among the .30 caliber cartridges mentioned, the .308 has the shallowest body taper, so getting stuck is, indeed, a little easier to have happen with it. It also has a wider included shoulder angle than the other two .30's mentioned, making it a little harder to set the shoulder back.
.308 Win/7.62 NATO is also a chambering for which small base dies are made. If you are using a small base die, that will also make it harder to run the case into the die and will work the brass unnecessarily and will increase the chance of a stuck case. Small base dies are sometimes useful to a first resizing of machine gun once-fired brass so it will fit any chamber. This is why the Dillon carbide dies for commercial reloaders are small base. But once fireformed to a rifle, and for once-fired brass from rifle chambers, there should normally be no need for a small base die.
Using good lube is always a good plan. In addition to the various commercial offering for the purpose, some guys looking for lower cost are now using white lithium greases. There are also commercial assembly lubes that have very high film strength and that are sticky like bar chain oil. STP mixed 50:50 with motor oil works well, if you don't mind the smell of motor oil. It can also be mixed with lighter lubes, like ATF and still seems to work, and it can be mixed with the aforementioned bar chain oil. There are lots of possibilities out there. Get some old cases and a beat up sizing die from a gun show and experiment to find what you like best.
If your cases have 15 load cycles and you've never annealed the necks and shoulders, you may find that reduces sizing effort enough to be worthwhile. It will certainly extend case life if the pressure ring isn't getting too thin.