850 is a bit high for a Smith carbine. Check out CDNN, they have blow out prices on the optics ready variants.

The Colt is the standard by which all others are judged. However, the extra money that one pays is geared towards testing and standards designed to make a better combat weapon. Since coyotes don't shoot back, you should be fine with the S&W, though the Colt will hold resale value better.

Honestly, a blow out priced current generation Mini14 - see also CDNN - will also do fine for what you want. They're easier to clean and have fewer small pieces to lose.

M4 carbines are designed to be a relatively compact weapon useful when going in and out vehicles, in urban combat, and have collapisble stocks to fit various users and users wearing body armor. None of that is really relevant. They are not designed to be precision weapons. If that is what you are seeking, then what you want is actually an A4 type rifle - longer barrel, flat top, fixed stock. You can probably drop critters out to 500 or 600 meters with a good one. In the tactical community, it'd be a DMR - designated marksman rifle.

Though if you find that you want to shoot coyotes at night, the flat op ARs will be easier to use with something like a PVS14 and an electro-optical device than the Ruger offering.

You need the 1:7 twist barrels primarily to fire tracers and relatively heavy JHP rounds such as used to increase lethality when fired from short barreled carbines at close range.

For coyotes, I would think that M193 type(55 gr) fmj or lighter JHPs would be fine. Some 1:7 guns don't do well with bullets under 55 grains.

Also for what you're spending on the Colt, you could get a Sig 556 from CDNN and they now give you a free Sig .22 understudy rifle for it with it. The Sigs are heavier, but easier to clean than the ARs and are quite accurate.