Broadly, you can consider all of them in the same general catagory.
I shoot all three, and believe there is a definite difference between them.
The 25'06, in hunting weight bullets probably has more versatility, and, at least on paper, is better able to handle larger game at longer ranges.
If weighing the relative merits of a 6mm or the 243 Win. off the shelf; I would go with the slightly larger case capacity. Depending on your barrel length, and bullet selection, it may not matter very much? But, the 6mm does have an edge.
Getting to the 24 versus 25 caliber debate, in a factory chambered gun, you will see heavier bullets available in twenty-five caliber. If that suits your mission, then that's the way to go. For large predators out to 400 yards or so, there is not a heck of a lot of difference between all three. All three can benefit by the Ackley improvement, so to say that the 243 Imp. is better than a 6mm; you can punch the 6mm to Improved demensions and it's a stand off.
Average accuracy potential probably favors the 243, to some extent? I just have a soft spot for a 6mm Remington, good all around choice; varmint to deer.
You cannot go wrong with any of the above.
Good hunting. LB