.22/250 is a hot rod .224"

. You however are not shooting gophers at 400yards. You stated Coyote at or less than 300yards. At this range,........ here's the real world numbers for your target type chosen .
Its a windy January morning and you are set up 300 yards from your foxpro call. Its -8C give or take a degree, and you got 15mph on your beam, heres what it's going to look like when you squeeze of on that Coyote. I've used Winchester ammo with the exact same bullet as a bench mark comparison, apples to apples shall we say. Enjoy.
200yd zero, gives a 300yard drop of 7.1 and 5.2 energy remaining at 300yds wind drift, 15mph @ 300yds
.223Rem 55gr Winchester BallisticTip 55grs MV 3240fps 7.1" 559ftlbs 17.1"
.22/250 Rem Winchester BallisticTip 55grs MV 3680fps 5.2" 746ftlbs 14.5"
You can see the 22/250 is superior. But will the coyote really know the difference in terms of drop and drift, or will it depend on the zero of your rifle, its inherent accuracy, and your marksmanship this day?
The .223 is way cheaper to shoot. Way more ammo types available. Less muzzle blast. Longer barrel life and on and on and on. If your target was very short like a prarie dog or crow at 350 yards, the 22/250s laser beam trajectory is superior and help ensures a hit with a little range estimation error. The 22/250 is a sweetheart if for nothing more than the look of the case. The .223 is boring. It looks like a miniature .30-06.
To compare two larger calibers likewise in an age old debate you would ask is a .30-06 good enough for Whitetail @ 300yards, or do you need a 300WSM? No you don't, not inside those parameters. So.....
For an animal the size of a coyote,...well..... you be the judge of what you really need. Both energies remaining are sufficient to dispatch a coyote humanely.
Sorry for the numbers a little confusing to extract, it didn't look like that when I typed them.