I think you can fire 4 aimed shots faster from a bolt action.

I agree with Al333.
If you need to reload your double fast I believe you are best to learn to do it with the old method and not need a new do-hicky.

If more "fire power" than that is needed a bolt action is probably the way to go for power levels over a 338 mag.

For those hunting game which can be dealt with at 338 mag level or less, a good semi-auto Browning is going to beat about anything else.

But that's just my take.
"Your mileage may vary"