Free: Contests & Raffles.
I have both. I like the 243 for bein able to hunt deer should I ever want to. the 250 is a bit chaper to load for but is also a bit tougher on barrels.......both are hard on coyote. if you really want to reach out and smack em' give the 257 roy a peek.
My advice is just pick one and get good with it. 250,243... doesn't matter much. the dog isn't gona know the difference. If you already have a 243 shoot it. I think you are just looking for an excuse to buy another gun, in which case just buy it.
I shoot 223, 22-250, 243WSSM and 25-06, when I don't want to take chances of losing a wounded coyote, I take the 243WSSM or the 25-06. My 25 is a Tikka T3 and it simply an outstanding carry rig.
I guess I don't understand how recoil is an issue until you get up to .284 or larger..... Actually most any of the calibers discussed here will kill the dickens out of any coyote, just depends how well you hit them. Coyotes are tough and unless you hit them well, it don't matter what you are shooting..... I actually think the scope and lots of practice shooting is a bigger consideration when coyote hunting....