If you believe the loading data, them little 40 grain and lighter pills can be made plenty speedy in the .223, but then you flip the page and look at the .22-250 data for the same slug.
I've got both, AND in several different rifles, single shots, bolt guns, and semi autos. The .223/5.56 is the ammunition that takes up the most room between the two, fifth in line behind .30-06, .308, 40 S&W, and .45 ACP.
You'll end up with both. Neither of 'em will keep up with the .220 Swift, and the .22-250 Ackley is right there with the swift, BUT, when the wind kicks up, I still, after all these years, pull out the .308 with a 130 Speer HP, .257 Roberts with 75 gr. hp, or the .270 with 100 gr. HP. THOSE three rounds truly make "red mist" on chucks and make really long range shots in difficult conditions a LOT easier.
If you're restricted to one round for now, go with the .223. The rifling twist will allow you to shoot bullets up to 60-65 grains just fine, something not always possible in a .22-250, cost per shot, as well as space and weight savings between the two rounds still gives the nod to the .223. It'd be my choice for a 'starter' gopher gun.