A .30-06 will do better with heavier bullets than will the .308, should you ever decide to chase something larger than deer.

However, autos can be very particular about ammunition, particularly in terms of overall dimensions. Your old .308 caliber bullets for your .30-30 are likely to cause you nothing but trouble used in an autoloader. As well, start playing on the light or heavy side of what bullet weights are available, and you're likely to have feeding problems as well.

My .308 reliably chews through anything in the 147-168 gr range, as long as it's seated to factory specifications and loaded between 2700-2900 fps. I once loaded some 190 gr for it, which ought just as well have turned it into a single shot for all the feeding and cycling problems I had with it. Lesson learned.

On the contrary, my bolt guns could care less what I'm loading. The .30-06 comes in many more "flavors" of bullet weights in factory loadings for a reason - the .308 only has so much case capacity, and when you stuff a looooong 200 or 220 grain bullet into a .308 case, it comes with an associated loss of powder capacity.