Since the OP already made his choice, I'll use this to back him up. I love a .243 for coyotes and smaller deer. I have shot all of my coyotes since I was 14 with the same .243 loaded with the 75 grain Vmax. The only time I switch the load is during deer season, where I run the Barnes 80 grain TTSX. My rifle loves the bullets in the 75-85 weight, and hates anything else. This rifle is getting passed down to my little brother this year for his first deer hunt at 13 years old. For coyotes I have gone to an 18" Sig M400 AR, but my deer rifle graduated to a 6.5 Creed. I loved that .243 and will probably buy another in the future with a twist rate to handle the 105 breed of VLD bullets. Hope the new rifle works out for ya, I don't think anyone could be dissapointed with a .243!
The 243 is a fine round and i think historically a little better for accuracy, but that said the 25-06 is far more versatile duz everything well , not great but well,,, better range and velocities just lacks the benchrest accuracy that most 243 have ! Since i can have both thats great but if i could only have one it would be the 25....