Like 30-378 said, the 25 is really over kill on yotes. It does have a time and place though. If its windy or the range is over 500 yards, it does have a place.
The advantages are that it will sling a 85g bullet 300fps faster and that results in flatter trajectory, more energy, more retained velocity, and less wind drift. Pretty much kicks it butt all the way around, but a coyote isn't gonna notice the difference. The only disadvantage with the 25-06 I see is burning roughly 10g more powder.
For coyotes/deer I dont think theres a better standard cartridge then the 25-06, but if solely for coyotes the 243 is very very hard to beat.