I can see downloading an 06 for a kid or woman but not a 7-08. Even full power 7-08 loads are mild. However, either one, .243 or 7-08 will do nicely. Both are deer killers.
Mild is relative. My boy at nine years old preferred a downloaded 7mm-08. I loaded a bunch of different Varget charges under a 120 BT and let him pick the charge he could handle. It was the next to lowest charge. Since he got to pick he had a sense of ownership.
P
