I have a Remington 700 and it's rate of twist for the 30-06 is also 10:1.
The only thing that I will add is that, in today's market, bullet design seems to go hand-in-hand with bullet weight.
For example, your typical older-style 180 grain jacked soft-point bullet is not going to be nearly as long as the new-style 180 grain Barnes Triple Shock. Alot of these new "NASA Engineered" bullets are significantly longer for their weight, so you should take this into consideration.
Granted, this might not make a difference up to 180 grains or so in a .30-06 as it would if it were a 200 or a 220 grain bullet, but then again it might.
Also keep in mind that we are not talking about accuracy here, but rather just bullet stability.