Personal opinion only, I don't think there's enough difference to make any difference. I usually do sort of a combo of the two with my Ariens snow blower. Letting the tank go low on gas (or siphon most of it out), I add a shot of Stabil to the tank, let it run for about ten minutes or so until it gets good and warm, then shut off the gas valve on the tank. The bowl empties & it stalls, then I drain the oil & refill it, pop the plug out, squirt some ND 30W into it, turn it over a few times with a cloth over the plug opening, put the plug back in, refill the oil, & consider the engine done. After that it's just a couple grease fittings, some WD40 on linkages, etc, oil on the movable metals, & store it. It takes about thirty extra seconds next spring to start it, but after coughing once or twice it springs to life and gives me yet another year's service. Bought it in 1979. Only part ever replaces is the throttle cable and the rubber-edged wheel inside that spins the drive wheels. I especially love being able to "start & go" in the spring that way. And it doesn't rust. Oh year, I replaced both belts a few years ago too - boy is that a b_tch of a job! But, it's a faithful ol' gal, still full of piss & vinegar.
If there's no gas shutoff (lawn tractors, etc.), I still do the same thing but I leave a little more gas in the tank, maybe an eighth to a quarter tank. Oh, and pull the starter cord just before storing it to be sure the valves close - set the choke full on; keeps moisture & spiders out of the mechanisms.
I guess it mostly depends on where you store it. If it's got a safe place to winter over, fine; but NEVER leave gas in anything that's near sparks or any source of heat! There you want to empty the tank completely.
HTH,
Pop