I've never even fired a 223 rifle. I always thought the cartridge was a bit too "generic" for my tastes. I like "weird" ones. That's why I bought the 204 when it first came out. It's not unusual anymore but it was then.
I've killed and seen killed a ton of woodchucks with the 204 and 22-250 though. For the most part, they do about the same damage, with a slight edge to the 22-250, depending on the shot placement. Many times, you'd never know the difference.
Being that the 223 is sort of like a 22 caliber .204, I assume it would be very similar in its effect. Almost like the illegitimate love child of a .204 and a .22-250