25-06 is a super cartridge for coyotes and deer. I started using it when I was 14 I think. I've had 4 of them over the years and put far more thousands of rounds downrange in those 2506s then probly all my others combined. It was my 1 rifle for everything back in the day except for elk, which I've always used a 7 or 300 mag of some sort on. Its what got me started into LR shooting, so I kinda have/had a soft spot for the 25-06. The 4 25s I've owned in order have been, a Ruger M77 MkII stainless/synthetic w/brake, winchester model 70 classic sporter, rem 700 BDL wood/blued, rem 700 ADL w/24" light varmint shilen barrel on it. All 4 were extremely accurate for being factory sporter barreled rifles, except the shilen barreled 700. All would shoot most any bullet/powder combo less then 1" at 100 yards from a bench, and the pet loads did 1/2 MOA from every rifle with severl different bullets. One of the lease picky cartridges I seem to load for in my experience. Matter of fact, my old win 70 classic sporter in 25-06 still holds my smallest 3 shot group at 100 yards to date, it measures a whopping .043", shot with 117g SBTs over H4831...My triple deuce has never even shot a group in the .0s, few in the .1s, and lots in the .2s, but thats been my only .0s group in my short life of 25 years, lol.
Anyways, I've tried 90% of the bullets out there and my favorite are the NBT's. There cheap, accurate, have fairly high BCs for hunting bullets, and they just plain work and kill stuff... Killed lots of coyotes and enough deer and few black bear with the NBTs out to a fair poke to know it means serious business. I never had any,coyote,antelope,deer, bear, or elk get away from the 2506, from 50 out to 600 yards, including 3 black bears with the closest being 375 yards. My sister even used it to take her cow elk at 300 yards with a 100g NP that I handloaded for her years ago.
For a factory round, its tough to beat a 2506 for a great longer range dual purpose yote/antelope/deer round out to at least 600 yards with the 115g NBT, I'd take it another 100 yards out to 700 if I had to, it would do her, coyotes 1K, far as you can hit em... Only thing that is better IMO, would be a 6.5mm of some flavor, say a 6.5-06, only becuase of the super BCs that they provide over .257"s Those 140s are tough to beat for a LR deer round, and the 95g vmax or 100g HPs would suffice for coyotes, or you could go the 120g NBT route and have the dual purpose bullet going for ya both on deer and yotes.
It just fits for a dual purpose cartridge for longer ranges. 243 is the better coyote round strictly for coyotes, throw deer in there, 25-06 gets the nod, now the 270 is a great deer round as well, I was gonna get one instead of the 25-06 when I was deciding what I wanted when i was 14. But it just seemed it was to heavy and big, kicked to much for steady use on coyotes. I went and bought the 25-06 and never looked back for about 6-7 years. Then I got a 7 RM for LR deer and bought a 243 for use on coyotes. Dont own a 2506 anymore, but I still love em to death and will always recomend them to someone looking for a dual purpose rifle/caliber. If your not shooting deer past 300-400 yards, then the 243 will work in most cases as well, I just like that little extra MV and bullet weight, with a little more thump.