Allen, to be really honest with you, I don't really know which one is better.
Like your saws I have this problem with my snowmobile. In the winter time I use it long and hard and pound the miles to it. The when the snow melts it sits...and sits...and sits for 9 months or so.
Now I have used Stabil in my snowmobile gas in the past, and I have also just let it sit with nothing in the gas. To me it seemed both had the same result. The carbs would varnish up with bad gas...and while the sled would run, it ran crappy. It did the same thing with stabil in the gas.
I no longer use stabil in my gas tank come Spring. It seemed to me just running old gas in it made the engine cough and sputter for awhile, but not nearly as long as running a whole tank of gas filled with stabil. Now they do recommend that sled owners use a fogging oil. You spray your carbs with it come spring, and its supposed to keep air and moisture from forming inside the engine as its stored. My results with this have been less than spectacular. Like the stabil, it took forever to burn that stuff out of my engine.
If you are still confused Allen, you should be, because I just don't know. I am just telling you what I have had for experience with storing my sled for long periods of time. I have yet to find out a truly good solution to my long-term storage problem. Its frustrating because its a $9,000 dollar snowmobile with a pretty technologically advanced engine, its in my best interest to store it properly, and yet no real good solutions seem to exist. I can see you are in the same boat with your chainsaws.