I've put a lot more .223 rounds downrange over the years, but I'm enjoying the .204 a lot! I've got the little CZ varminter, topped by a simple 12x Leupold. Do my loading with Wilson dies, and it's just a hoot on our local rockchucks!
My youngest son giving the .204 a try at some rockchucks up on the cliff above the orchard. It worked just fine...
No recoil. 3800 fps with 40 grain Hornady V-Max bullets and excellent accuracy. It's fun to see the impact of the bullet on the animal. The crosshairs never even come off target. I like the .204, but if a guy chooses a .223, he's just got the more popular cartridge, and that has some advantages. My oldest son uses a .223 Bushmaster AR-15 varminter with a 6.5-20x scope. It's a varmint zapping machine!
I don't think there's a huge amount of practical difference between the two in the field. They're both fun and effective.