All the data I've seen says 30-06 and 300 mags are pretty much equal with 200-220 gr bullets and are about the minimum. The 375 seems to be the next step up and nothing in between seems to really matter.
Here is a good read. I've read some of Finn Aagaard's test results, but don't have a link to his data. It is fairly close to what was found here though.