I'll be the second to be busted in the chops but here are my thoughts:
If you are reloading the edge goes to the 243. For example if you are shooting the Hornady V-Max you have the 58,65,75,and 87 grain bullet weights to choose from in the 243. Whereas Hornady only makes the VMax in the 75 grain for the 25 caliber. If you do a quick check over at Midway you will see that they stock 119 different bullets for the 243, but only 59 for the 25 cal.
Factory ammo is no different. There is almost double the factory ammo selection out there for the 243.
If I were ONLY shooting coyotes, it would be the 243. If I were ALSO going to use this rifle for deer sized game, then I would take a long hard look at the 25/06.
Or else, better yet, just buy one of each! They are both great calibers and neither one would be a mistake
Calcoyote