i will use continuous shooting if using AEB.
'i realised it refocuses each time' you said it yourself. that's the difference.
it's just like firing a machine gun. you fire continuously (assuming you're aiming at only one spot), you're more likely to hit the target more times at the same spot.
if you're using handgun instead, you might miss the spot by a little, which means you're more prone to handshake.
i mean, this is my theory, others may not agree.
hope this helps.
If you are on handheld, use the highest speed continuous you can use
If tripod, it's okay to just focus once, switch to manual, and also use the PRE mode of white balance and shoot all the different exposures