First off, this article assumes the animal will be stopped with only two shots, and that is rarely the case with buffalo. Having said that lets assume a buffalo will be stopped with only two shots and that as Monty says "the key word is AIMED shots" in my opinion, the key word is just as important all shooters no matter what type of rife you are shooting in that situation. With that in mind, I would say for the first two AIMED shots the second shot would be easier/faster when only recovering from recoil of the first shot and pulling the trigger on the second shot by simply changing triggers than having to work a bolt after recovering from the recoil of the first shot and getting back on target for the second shot.

Now lets assume the buffalo needs four shots to stop or turn. In this case it has been proven by the PH testing that a man who is good with a double rifle is at no disadvantage for four shot to a man that is equally skilled with a big bore bolt rifle. First shot being equal, while the second shot with the double is faster, and about equal to the bolt rife shooter for shot three and faster again for shot four with the double. The speed is of no value if the bullets do not go where they will do the most good.

At shoots by the DRSS, this has been tested several times and the double has won every time,
This shoot is done with the double rifle loaded, and the both rifle with one in the chamber and three in the magazine. The kill zone is an 8 inch black target at 25 yds with a 2 inch ten ring in the center. This allows a max score of 40 points if all four shot hit the ten ring, and any shot that misses the black is not counted. The shooters are all individually timed with a stop watch, timing starts when each shooter fires the first shot, and stops when shot four is fired, with everyone shooting at the same time for noise distraction. Timed and scored for accuracy!

I took third place with four shot fired in four seconds flat, and I forgot that the rifle I was shooting had an automatic safety, and tried to fire shot three with the safety on costing me time. My score was 36 out of a possible 40 points and if I had been facing a lion charge that safety could have cost me my life. Even with the safety I beat every bolt rifle on the line for time, and the only both that beat me for score was slower that I by two seconds.

I was severely chastised by one of the members here, for having a double rifle that I had owned for some 8 years, with the auto feature not disengaged, when I had been recommending the auto feature be disengaged to others for years. My only excuse is that was not my go to DGR, and procrastination was my mistake.

In any event IMO the double is faster for the first two shots than a bolt rifle but the bullets must go where they do the job, or the speed is a moot point