The Heel You Can Replace, and the Measurement That Should Decide
Most discussions of sock heels compare the flap-and-gusset with the short-row heel and stop there. Two things get left out, and both are more practical than the comparison itself: the heel you can replace, and the measurement that should decide between them.
The afterthought heel: the one you can replace
Knit the sock as a plain tube with waste yarn where the heel goes, then come back, pull the waste yarn out and knit the heel into the opening.
Its great advantage is repair. Heels wear out first, always, and an afterthought heel can be unpicked and replaced without touching the rest of the sock — turning a worn-out pair into an afternoon's work rather than a loss. It is also the natural choice for self-striping yarn, since the uninterrupted tube keeps the stripe sequence unbroken.
The trade-off is depth: like the short-row heel it has no gusset, so it fits a high instep less generously.
The instep is what should decide
Depth is the real difference between the constructions, and the foot measurement that matters is the instep — around the arch and over the top of the foot, not the ball.
A high instep needs the extra fabric a gusset provides and will find a short-row or afterthought heel tight across the top. A low instep will find a flap-and-gusset heel slightly baggy at the ankle. Neither is a defect in the method; they are different shapes, and feet are different shapes. Measure it once and you will know which family of heels to reach for ever after.
The other two, briefly
The traditional construction. You work a rectangular flap back and forth over half the stitches, turn it with short rows, then pick up stitches along the flap's edges to form the gusset, decreasing back to the original count.
It produces the deepest heel and the most fabric where the shoe rubs, and it is usually reinforced with a slipped-stitch pattern, which doubles the thickness in exactly the place socks wear out. If you wear socks hard, this is the construction to learn.
The short-row heel is a cup worked in short rows over half the stitches, with no picked-up stitches and no gusset — faster, tidier, less yarn, and very like a commercial sock heel. It is shallow, which suits low and average insteps.
Both are covered in more detail in turning a heel; the point here is only where each one sits on the depth scale.
The row counts matter here
Heel construction is where row gauge stops being optional. Flap depth is specified in rows, gusset decreases happen every other round, and short-row heels turn on a stitch count that assumes a particular proportion.
Working these to a row count when your row gauge differs from the pattern's produces a heel of the wrong depth. The row counter is genuinely useful through this section, and recording the counts you used makes the second sock straightforward.
Reinforce it
Whichever construction you choose, the heel is the first thing to fail. A slipped-stitch reinforcement, a strand of fine nylon held alongside the yarn, or simply a yarn with nylon in it all extend the life of the pair considerably.
The cost is negligible and the benefit is measured in months of wear.