I have wondered the same thing. I would guess that picking up both sides would give you a thicker bump or ridge.

I do Elizabeth Zimmerman's heel...and keep the sides of the heel flap in garter stitch. That is, knit the knit rows. On the purl rows, knit the first four and last four stitches. You also slip the first stitch and purl the last stitch on each row, which gives a pretty and useful braided edge....making it easy to knit up, when the time comes. You'll see, once you've completed a heel flap like this, you will be able to see that if you pick up just one side of the braid, it'll leave a nice edge to the garter stitches.
When there are half as many garter stitch ridges as there are stitches on the heel flap, turn the heel.

I was told to pick up both sides of the stitch to make it stronger.

Tami

You can pick up the slip stitches in two ways, one in which you pick up under the complete slipped stich, and the other picking up the outer stitch only. The second method adds a decorative touch to the heel gusset. I tend to use the single slip pickup on socks that are fancier socks, and when the pattern can be seen! LOL!!