I get slightly better results doing it by PC/Cyclo and I like it better

Better chance of uniform coverage with all those orbits-per-minute (especially with the Cyclo's overlapping pads).
Removal by hand/machine is usually pretty much a toss-up as you need to follow up a machine removal by hand anyhow. But again, consider all those OPMs...do you really buff as thoroughly by hand? OTOH, does it matter?
But *in some cases* doing eveything by machine gives me a noticeably better LSP effect (note that 99% of the look comes from the prep anyhow). Waxes like #16 simply work better with more aggressive application techniques (which better facilitates the "paste wax that turns liquid" effect) and sometimes the additional burnishing that removal-by-machine provides can impart a little better luster.
Doing a "pseudo spitshine" while applying/removing by machine gives me tiny spherical beads that just *barely* contact the underlying panels; it's like a zillion ball bearings sitting on the paint. I simply can't get that effect to the same extent by hand.
Straight/elliptical/circular....doesn't matter as long as you don't instill marring- how *can* it matter? Likewise,nobody's ever provided any compelling evidence that the "up-down on the sides/back-forth on the horizontals" makes any difference either (LSPs don't have a "grain", at least not to the naked eye or with up to 30X magnification; I've looked for it).
As for the manufacturer's directions- I'm sure glad Mike Phillips challenged me to ignore them and let Souveran set up before I buff it off; wish I'd tried it years ago.