That is a tough one. Both calibers are have their strong points. The .204 is flat shooting, almost no recoil, easy on barrels, and easy on powder. The .223 is also flat shooting (not as flat as the .204), carries more energy for larger critters like coyotes, and surplus ammo.
With that, I would get the .223 if it was for an AR platform and it was my first varmint caliber. I have thought about getting one, but I already have a .223 AR (Bushmaster Varminter) and a .308 AP4 (DPMS). I also have a .22-250 in a Rem 700 VLS. So, I think a .204 would fit nicely in there.
It takes a lot of discipline not to blow through a 20 or 30 round clip when you are at the range. I imagine it could get more expensive with the .204 than the .223.