I'd ask what "practice" means here... I practice (shoot every few months- all reloads) and both these calibers are usually taken to the range. Actually the 22-250 is an Akley Improved and so I shoot standard rounds to fire-form brass for it on about every trip down. That said, I never shoot more than a few rounds of any rifle (including my 6.8 SPC and 5.56 ARs)
Occasionally, there is the long day of working up a new reload and that particular gun gets shot more while working the load up proper. But still, rarely more than a dozen shots are taken on those guns I'm working a load for. I then prefer to shoot cold barrel when I get a load tweaked (after several times to the range). So those guns (already dialed in) are shot 3-6 times at most. Sometimes I'm just cleaning the rifle, taking the first "fouling shot", and confirming my zero (3-4 shots do fine for that).
I say the above to demonstrate that although I shoot pretty regular year round, I don't fire a lot of rounds. In this case, given the OP's question I'd give serious thought to whatever caliber I MAY ALSO find useful to me given what I hunt. I'd give the 22-250 the nod in my own case here.
It also gets cheaper to shoot a 22-250 if you reload... and if you don't run hot charges ANY brass will take many reloads (*if you anneal every few loads). I mostly prefer the 22-250 as it closer replicates the ballistics and speeds of my larger caliber rifles (I am practicing for). Yes, you can shoot SLOW 223 rounds long-range, but it's more of a "lob" than a "laser" and I find it better to "practice" with a rifle with similar ballistics to my larger calibers. The 22-250 is capable of use for longer range hunting putting some SPEED on the .223 heavies (*with the BC needed to "keep on going"). Reloder 26 helps here too
All this said, I have an amazing 223 bold gun for shredding p-dogs and I use it WITH the 22-250ai on those rare, but fun hunts. The 223 shoots 40g at 3850 FPS- point and click out to 200 yards- a FLAT laser rifle for sure. The 22-250 shoots 75g about 3350 BUT with 300 yard head shot range ability and better in the wind (especially here in Kansas).
BOTH are excellent "practice" calibers without a doubt but the 22-250 can kill way out there and for the larger bullet and speed, I'll take the (lower twist) 22-250 if it came down to one gun more usable in the field I typically hunt in AND given my "practice" preferences and reloading capability.