This topic is a pet peeve of mine, as another error in the gun culture. Even before there was a www, there were guys posting on the usenet that the 223 was a 200 yard gun and the 22-250 was a 400 yard gun. This is unqualified non sense.
The factory 22-250 rifles have a slow twist rate, typically one turn in 14", and the factory ammo is make with the weak 1889 7.65x53mm Mauser case head built with a large Boxer primer. The 22-250 Rem is registered with SAAMI at 65kpsi and with those large Boxer primer pockets, it can be handloaded to 67 kpsi.
While a .223 may be registered with SAAMI at 55kpsi, is good for 75 kpsi with handloads for an individual rifle and still have long brass life.
So using the bullets the factory 22-250 will shoot, and running at the pressures that allow long brass life, the 22-250 has the ability to push a 50 gr Vmax at 3966 fps
Meanwhile a 223 with the same bullet and barrel length and long brass life constraints, will do 3700 fps.
A 50 gr Vmax slows down from 3966 fps to 3700 fps in 50 yards.
That does not mean that the 22-250 has a full 50 yards more range, just that much more velocity.
Now, if one re barrels a rifle to 22-250 with a fast twist barrel, 22-250 chamber, and uses Lapua 308 palma cases [small primer pocket] sized down to 22-250 and the necks turned, then at 90kpsi and with a 90 gr VLD bullet at 3283 fps.
The 223 with the same constraints gets 2781 fps.
A 90 gr VLD slows down from 3283 to 2781 fps in 280 yards.
What does it all mean?
A) With the kind of 22-250 I have, and the kind of 223s I have, like 99% of the other handloading guys working up loads to the threshold of long brass life and then backing off a safety margin, the 223 is with in 50 yards of the 22-250.
B) But theoretically, 1% of the guys out there, might get 280 yards advantage.