I have shot quite a few caribou, a couple black bears, a wolf, and a few deer with a .250-3000 in a model 99a. The 1970's rifles had 1-10" twist barrels and I believe that is the best twist rate. I used both 87 and 100 grain Winchester factory loads as well as 100 grain Noslers for the bears. I really do like the little .250 and in a small bolt rifle the brass would last a bit better. Recoil is great.
I've never owned a .243 but it would likely do just as well but I decided years ago I didn't care for the round. Not every decision needs to me rational! I also have a CZ in 7.62x39 and my girls enjoy shooting it. I really think the recipe is a moderate cartridge that is accurate, has modest recoil so people shoot them well, and people don't try to shoot too far with them. I would never have considered buying a 7.62x39 a few years ago but the little CZ bolt gun changed all that and surplus practice ammo is so cheap, I only load hunting rounds. Make sure you glass bed it if you by a little CZ.
I would decide based on the rifle you prefer and your willingness to reload. Practice with the rifle and it will be an over achiever.
IMO, anything a medium cased 25cal can do with 100gr bullets a 243 will do just as well (or better, considering the slightly higher sectional density, and likely a better BC if comparing the same bullets). The 243 offers the option of loading some really light pills(eg 65gr vmax), which can make the recoil very tolerable for kids to practice with, especially if they are not full power loads.




















































