It depends on the ranges you ordinarilly shoot. I am a ground squirrel hunter in California and must hunt on ranch land, where sheep and cattle graze. I do not want a bullet to ricochet and I generally don't need more than 250-300 yards maximum for the bullet to perform. I have used .222,.223 and 22-250. I feel the 22-250 is too much gun for these small animals, although it has a greater range. Most of my shots are between 100 and 250 yards.
I have purchased a Cooper in .20 VarTarg for the ranges I like to shoot in. I still like the .222 because of its inherent accuracy, lower barrel heat, availability of good brass. I still have the .22-250, but only because .204s were unavailable in the mid nineties when I bought the rifle (set up by Darrell Holland: massaged Remington 40X action, Hart heavy barrel, McMillan custom stock). I like the rifle, but rarely use it for anything except coyotes. It is set up for 55-grain bullets, pushing them at around 3500 fps.
Keep in mind the barrel heat problem. The .22-250 displays too much barrel heat for hot/heavy shooting, so if the .204 helps in that arena, another plus.
And, the .22-250 uses powder somewhere north of 30 grains. I think I have the cases loaded with 32 or 33 grains of H4895 and use Nosler Ballistic Tips in 55 grains. The rifle shoots well with that combination, although other rifles in this caliber may like another set-up. Good for Coyote and the larger varmints. The rifle is fine for PDs, but you had better plan to take at least one other rifle to use after you clean the .22-250 and let it cool down.