Additionally, nobody has stated yet but shouldn't guards in charge oughtta hold their halberds perpendicular onto ground rather than leaning them on shoulder ? (onwards 12:09)
And not sure if there is only a 'true way' should I say, but while running one can also continue running while holding the sword on your shoulder ?
Adressing this a bit late, but hey.
Personal preference, really.
You do it one way or another.
For moving, leaning them on the should is much more comfortable, for standing guard... it doesn't really matter. If I'm really bored and nothing is happening, I'll put the stave perpendicular on the ground, to lean myself onto the polearm.
But as I said, you can do it any way you like. There's no one "correct" way to stand guard with a polearm.