SalemDawger, here is what you are asking:
best bullet in a 16" or 20" AR with a 9 twist vs a 22/250 with a 24" 12" or 14" twist barrel.
In otherwords, what bullet works best at 2850fps-3100 fps in a 9" twist or 3600fps+ out of a slow twist.
A bolt gun 223 with 24" barrel with 9"-12" twists are a different animal vs an AR when it comes to you finding a fast velocity load that will extend the range of the 223.
In my experience in shooting 9" twist barrels, the increased RPM's over the 14" twist does tend to have the bullet come apart quicker on p. dogs, so coyotes would be even more so with more mass and larger bones.
In my experience, the only poly tip bullet that I will shoot on coyotes are the 60g V max and the 50 and 55g Noslers. If you want to do some bullet testing so as to not maim animals, on the next coyote you kill, hang him up in a tree, back up and aim for specific spots on the animal, the shoulder and hip joint. Do your shooting from 100-200 yards, and you will learn a lot when you skin the hide off the aniamal when it comes do damage.
Of all animals that I have hunted, the coyote will take more abuse than anyother animal. Shot placement can be critical, and shots behind the diaphragm with a 223 AR(and many other calibers) will usually mean a lost animal.
On my Remington 700 SPS Stainless, I shoot the 55g Nosler at 3450 fps, and it simply does a great job, however this is not attainable on AR's, and not even close. 200 fps is a HUGE deal when it comes to killing power and the size of the temporary wound cavity that is created on a coyote at 200 yards.
Everyone is different in their thinking and experiences, this is why an open forum is great to discuss the success that they have had. I like a bullet that will expand and penetrate, this leaves a lot of bullets on my shelf for colony varmints, NOT coyotes. A bullet that is designed to completely come apart in 4" of ballistic gel, is going to fail for predators often, especially on quartering shots, to and fro, and I don't believe in the hose'em down theory...been there, done that.
So, trial end error on your part with various bullets will be fun for you to try. Several of my favorite bullets would be the 60 V max, 55g Nosler, 55g Sierra Spt. The two toughest 55g bullets are the 55g Horandy Sp and the Sierra 55g BTHP. Again, there is no room for error for hitting them behind the diaphragm. For shots behind the diaphragm, the 243 and 6 Remington are KING of the HILL. I had a lot of coyotes run off that had been shot behind the diaphragm with a 22/250, especially at yardages of 150+.
In my hunting experience, the vast majority of shots on predators would range between 80-125 yards. So, with these close shots, all it is going to take is shot placement. Coyotes are often shot while walking, trotting, and at a dead run which makes a shot hit behind the diaphragm to the hip joint. Also, don't forget that with slow velocities, you will be more apt to unzip a coyote as the yardage increases to 200 yards-250 yards.
Also, heavy AR triggers are simply no help in proper shot placement, I would drop a JP trigger in mine before I ever fired a shot. A heavy trigger with a right hand shooter will leade to the shot being jerked off to the left more often than not. So, the spray and pray is not worth a darn with a heavy trigger, with the exception that you have scared off multiples that you might have had a shot on otherwise.
SalemDawger, with your last year's experience compared between the AR and the 250, you might ask yourself why you need an AR? I sold 5 Colts over the years plus a total custom built Colt, and I never looked back...guess what???? I was asking myself the exact same question that you are asking now! I put the money into a Rem 700 24", 12 twist, 22/250 AI shooting the 55g what evers at 4050 fps...the holy grail of varmint hunting for me. It has been rare, really rare that I ever could have killed a coyote with an AR with it's multiple shot capability vs the bolt gun. However, perception would leade you to believe otherwise. While living in S. Ca, Arizona, and hunting in Old Mexico, we killed a huge number of coyotes.
Part of the joy in our hunting is trying different guns, loads, bullets, etc. So, this is just a hobby, make it fur for yourself and chase your own dreams of a perfect coyote arsenal.