I like the .30-06, but can understand one chambered in .308. I have an adjustable gas plug, bought a bit of the Greek CMP ammo, and reload so my issues finding usable loads for .30-06 is minimal. It uses a little more powder than a .308 but it feels right. Also, being able to handload and adjust the gas plug allows for a little hotter .30-06 load if needed, though honestly, I hunt paper and broken electronics with the M1 so I don't load hot. I do think the conversion scares a lot of people from a resale point of view. I wouldn't buy one I couldn't test first in .308. That's not to say it won't be just as reliable but I want to have it proven before I would spend the money. As for accuracy, honestly, I don't think there is much difference that can be blamed from one chambering to the other. There have been plenty of accurate .30-06 rifles out there and plenty of accurate .308 rifles. With all thats going on in the cycling of the M1, given equal quality parts used for both rifles, I have troubles seeing one be more accurate in general than another. Again I'm sure there are examples of very accurate rifles in both rounds.
If you don't reload I would look at which you have better access and price to the ammo you want to use. Surplus, while often not near as accurate, is about as cheap as it gets. If you have a way to get surplus of one in better quantity and for a better price than the other, that would be a big consideration. Reloading all but evens things out.
So really, just get what you like better and enjoy it. There isn't really a wrong answer here. For some the answer is different than others so get what you like.