Small Game, Predator and TrappingFrom shooting squirrels in your backyard to calling coyotes in Arizona. This forum now contains trapping information..
Only difference I see is that the 22-250 will give you, maybe and extra 100 yds or so, maybe a little more on a calm day. Fact is, both rounds will kill what you have mentioned and not look back. Take your pick, if you reload, cost is no issue, but however .223 is cheaper for the non handloader (had to say it, really wasn't on my mind until Ruddyduck mentioned it)
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I own both. The savage 223 heavy bbl is more accurate. But i take the 22-250 more often because it is a sporter bbl. It likes to shoot too. If you don't load, their is not that much difference in premium varmint ammo for either. A few dollars per box. I think the 22-250 is a little more versatile than the 223. But both are fine rounds and you would be suited well by either. I would worry more about what gun you get, then which round.
Range is probably the determining factor here. If you need really to reach out and something, then the 22-250 is probably a better choice. My advice would be to go for both!
Seriously though, I have and really like a Savage 12BVSS 22-250, a heavy barrelled varmint rig. Weighs in at over 10 pounds with the scope and all. That's great for taking to the range, or if the hike isn't too bad. But I can definitely see adding a lighter, short barrelled 223 to the collection. I think if you're going to be hiking a bit you're going to want a smaller/lighter rifle, which would take away some of the advantage of the 22-250, so why not make that one a 223. My two cents worth anyway.
The 22-250 is the superior round, if that's what you're looking for. With hand loading and practice, you can do just about anything you want with a .223 cheaper, without the threat of barrel erosion.
If you want to claim to have the absolute best .22 cal. gun, just for bragging rights, I'd look at the .220 swift.