Doubletap increases ROF by 20%.
Stopping power increases bullet damage by 40%.
Which of these kills enemies quicker?
Simple math.
Take an Skorpion bullet at long range, for example. You need five body shots to get a kill. Say that, if every shot hits, the time taken to kill with it is x.
If you are shooting at 120% of your normal ROF, it only takes 5/6x to get the kill.
If you are shooting with normal ROF, but 40% damage, each bullet does 28 damage. Since you only need to shoot 4 bullets, the time it takes to kill is 4/5x.
As 4/5<5/6, SP has killed quicker than double tap.
Take, as another example, the AK-47, within its max damage. It takes three body shots to kill with this, and the time again, is x.
At 120% ROF, we again have 5/6x. It needs the same amount of shots, but only 83.3% of the time.
At 40% damage increased, with normal ROF, each bullet does 56 damage. It takes only two shots to kill with this. Since you only need 2 bullets, the time is 2/3x.
As 2/3<5/6, you again have a quicker kill.
Finally, take a M4, at 30 damage. Four body shots to kill with this are required.
At 120% ROF, we see the same 5/6x.
At 40% bullet damage, and normal ROF, we only need 3 bullets. Consequently, time is 3/4x.
As 3/4<5/6, we again see stopping power is quicker.
While this assumes you are actually aiming, I think we can see that stopping power should be used over double tap.
There might be exceptions, but this definitely works as a general rule.
Stopping power increases bullet damage by 40%.
Which of these kills enemies quicker?
Simple math.
Take an Skorpion bullet at long range, for example. You need five body shots to get a kill. Say that, if every shot hits, the time taken to kill with it is x.
If you are shooting at 120% of your normal ROF, it only takes 5/6x to get the kill.
If you are shooting with normal ROF, but 40% damage, each bullet does 28 damage. Since you only need to shoot 4 bullets, the time it takes to kill is 4/5x.
As 4/5<5/6, SP has killed quicker than double tap.
Take, as another example, the AK-47, within its max damage. It takes three body shots to kill with this, and the time again, is x.
At 120% ROF, we again have 5/6x. It needs the same amount of shots, but only 83.3% of the time.
At 40% damage increased, with normal ROF, each bullet does 56 damage. It takes only two shots to kill with this. Since you only need 2 bullets, the time is 2/3x.
As 2/3<5/6, you again have a quicker kill.
Finally, take a M4, at 30 damage. Four body shots to kill with this are required.
At 120% ROF, we see the same 5/6x.
At 40% bullet damage, and normal ROF, we only need 3 bullets. Consequently, time is 3/4x.
As 3/4<5/6, we again see stopping power is quicker.
While this assumes you are actually aiming, I think we can see that stopping power should be used over double tap.
There might be exceptions, but this definitely works as a general rule.