It's been my personal experience that the .204 outperforms both the .223 (easily) and 22-250 (slightly).
The ballistics also support my observations, depending on the load/bullet and/or if you handload. It really is a much more efficient cartridge.
It's really not even fair to compare the .223 to the .204 but the 22-250 is closer in performance to the .204.
I own all 3 and each has their purpose but I reach for my .204's most times when I am heading out the door.
Believe it or not, the .204 typically bucks the wind BETTER than the 22-250 - again depending on the load and bullet. That is the upside of SPEED! It also has less muzzle blast and muzzle flip... In my humble opinion, it is easily the best of the 3 options.
--Duck911