My friend,
The .270 cases would be best because it is a minor neck process going down .020". Basically, you're simply going from .277" down to .257". Just do it in your .25-'06 full-length sizer and you're good to go.
Obviously, necking down from .30-'06 cases would require a major necking-down (from .308" to .257") and that would probably build-in some degree of case neck concentricity problem. Also, you would need an intermediate die, probably the .270 FLS would work, and it potentially would thicken your necks, creating a potential bullet release problem.
Anyway, the best case would be your .270s. Because .270 cases are considerably longer than the basic '06 case, you will need to trim.
The maximum case length on the .25-'06 case is 2.494", so you should trim .010" shorter than that; to 2.484".
When necking down, I heavily chamfer the outside of the case neck. This will aid the case necking process. I also very lightly oil the outside of the case neck. These two details also help in case neck concentricity.
Further, I would check the thickness of the case necks after alteration. There is an outside chance that the necking-down might thicken the necks. In this case, the necks would requite turnng. Frankly, I don't see this happening, but it's always best to be careful.
Necking your .270 cases to .257" is a minor handloading process, so don't worry over-much about it.
If you run into any difficulties, either address me on this thread or send me a PM. It would be my total pleasure to help you in any way I possibly can.
All the best,
Steve Timm