Too me it comes down to rifle action. Give me a good, light short action any day.
In reality the .243 doesn't give up much to the .25-06. A couple hundred FPS in comparable bullet weights and .014 in diameter. Factory 110gr .25-06 clocks in at about 3100 fps while factory 100gr .243's are at about 3000 fps. Not a deer in the world that will notice the difference.
As already stated, if you're game gets bigger than deer the .25-06 gets the nod due to the option of getting bullets of 120gr plus. But then again I'd pick a .260 or a 7mm-08 (short actions) over the .25-06 due to the fact that they comes in rifles I like better.
IMO, the only place the .25-06 excels is long, long range. If you're ranges are consistently over 300 yards AND the quarry is bigger than deer the .25-06 gets the nod.
Basically this discussion is the same one that goes on about the the .308 vs. the .30-06. The .30-06 is a little better with heavier bullets but they are basically interchangable in their uses. .25-06 ammo and brass may be harder to find and the .243 is available in rifles I like more and recoils a little less. Give me a .243.
CB