denjahn,
My two cents. I agree with all the above posts. Just came from the shooting range, where the new 204 is shooting so well it scares me! Since I'm playing hooky from work this morning, may as well chime in.
For coyotes and deer I shoot a 243 and a 6mm Ackley. Don't think the Ackley thing was worth the trouble for coyotes. On deer though, the Ackley shoots a 90 BT at 3540. (And, no, I won't tell you how much 4831 is in the case!)
I'm lucky enough to have shot near 10,000 rounds at PD's with 223s. For 90% of dogtown shooting, it is the king. If you can't hit that bad boy with a 223, it is usually time to move. On the other hand, 800 rounds with a 22-250 was enough to make me get rid of it. Never again.
So, I jumped on the 204 bandwagon, trying to find something a little more than a 223, without the recoil and barrel heating nuisuance of the 22-250. Hope this 204 Ruger will do that. But I've found it needs to be loaded down a bit.
Hornady factory ammo that I've shot is too hot to shoot freely and often. Recoil is much less than a 22-250, but suspect you'd be right back into the barrel heating problem.
Settled on loading Hornady 32's at 3875 with 26.5 Benchmark, just a half grain above Hodgdon's starting load. I think I can shoot a hundered an hour and not worry about barrel heating. Hornady 40's at 3700 with 29.0 of BL-C2 is a little hotter, but still pretty mild.
My bread and butter 223 PD load is 40 Blitzkings, 27.0 335 at 3500. The question is -- will the 204 reach out more than the 223? Don't yet know. We'll find out this summer. In theory, a 40 grain 204 bullet at 3700 should have an advantage over a 40 grain 22 caliber bullet at 3500. Likewise, the 32 going near 3900. If the 204 proves to be nothing more than a 223, so what? I've had fun and got to get another shootin iron!
The 222 Rem Magnum is a little more case than a 223, but loaded to the same pressure, you're shooting the same bullet at the same velocity. Yeah, you can squeeze a 100 fps more out of it, but why? The old 222 Remington has a little less case capacity than a 223, and in the real world it does what a 223 does. Right now, 222 Rem Magnum brass is hard to find due to guys fireforming 204s. And, it costs $190/thousand versus $130/thousand for 204 brass. Factory ammo are choices are limited for both 222s, store inventory nearly zero. If you find it, it won't be cheap.
My vote, get a 204. If a 22 is in your plans, get a 223.