I heard back from Doug. Here's what he said:
I don't know. I have always sold separate case holders for those cartridge sizes. I don't think they have the same body taper because they have different lengths. .308 & .30-06 appear the same way, same diameter rim and shoulder, but different lengths between the two and most definitely require different case holders.
Doug Giraud
_____________________________________________________
So if even THA' MAN isn't sure, then I guess the only thing to ask before I have to cough up an extra $30 and order both case holders is: has anyone tried trimming both cartridges with only one of either caliber's case holder?