First how many 800 yards shot does one encounter? I don't see many at all most are much closer and my long range shots are in that 450-600 yard range, also do you want just dead coyotes or pelts? Caliber selection could make a differance as well on your end result. Next would be cost of gun? There are some on the market that would make good long range guns but pushing that 800 yards range with consistancy will take a good rifle.
I would opt for the 25-06 if you feel your going to get "enough" shots at that 700-800 yard range, I know most of mine will be under that 600 yard mark so I like the .243 with less recoil and seeing more through my scope, a gun doesn't have to be blazing fast to be a good long range gun, it must be able to repeat time again point of impact at those ranges.
At 800 yards here is wind drift at 10 mph
.243 80 bullet 73.5"
.25-06 115 Nosler Bal tip 54.2"
.284 bullet 150 grain at 2890 fps 47.4"
Your talking 7" differance between the 25- 06 and the .284, the benefit from the 25-06 is 7" is something that is corrected with a good scope and turrets, so then one needs to look at barrel life, cost of ammo or reloading componants, the 25-06 has cheaper brass, burns less powder on average, and bullets some cheaper as well.
Now me with my .243 I shoot out to 650 yards my drift is 42.3" again very liveable with the scope I have on it so it works for me real well, I can either "click" in the drift or with my mil dot scope I'm looking at 1.8 mils at 650 and 1.6 mils correction at 600, so again not a big swing for me, clicks with 1/4" scope it means at 650 I need 25.3 clicks or turn dial to 6.4 on my dial at 600 yards I need 23 clicks so I turn the knob to 5.8 and I have my windage darn close.
I have my cheat sheet with both from my bal program, if I need a quicker shot then I use the mils for both windage and elevation or if the coyote is sitting tight and gives me time to range and dial I will.
Each to his own but my heavy barrel .243 does a great job at that 400-600 yard range, for a factory gun and finding that right load I couldn't be more happier, it will print at 1" or less groups at 200 yards.
My 25-06 my futherest shot was a white tail at 455 yards with a nosler 110 accu bond it did the job well.That scope has the BDC type, if I had it to do over I would put the mil dot with turrets on it as well, a very functional and gives you 2 options I like it much better than the BDC type.
Good luck with what ever you decide on.