Magnums offer no more killing power per say at close ranges than its little brother and actually can cause problems at close ranges, the high velocities can cause bullets to blow up at close range, and lack penetration, so then you go to harder bullets and then you start blowing tiny holes in deer. A 30-06 can be better than a 300 mag at close range but vice versa at long range.
Magnums are intended for long range. But I doubt any deer will stop a 300 mag at close range, but get into bigger game and I bet you will see what I am talking about.
We took 2 huge hogs with my friends 300 at close range, the mag did not go through them, but I bet if we would have shot them at 150-200 yds it would have gone through.