Gretch,
The only reason to use Stabil is if you're going to be storing the gas for some time. The new fuels tend to degrade just sitting in the can for as little as month, and their ethanol content actually attacts water vapor. From what I've been told, stabilizer will extend a good fuel's shelf life for up to 6 months. The issue with 2-cycle mixed gas is that hobbyists and homeowners are usually in the position of having to hold some in the can for more than a month between saw sessions. You can't put the leftover mix in your car or truck, and, unless your town has a drop-off for oil and gas/oil mix, your only other alternative is to either let it evaporate or burn it in a controlled fashion; neither is a good choice for our climate, and both are often illegal. Stabilizer in the stored fuel is then a good option.
I buy gas, and then mix in the oil as I need it at no more than a half-gallon at a time. That way I never have much of a "mixed" leftover problem. I don't put the stabilizer in until I know that I'm storing those leftovers.
My other small engine units (generator, log splitter, snow blower) use different fuel line material than those small tubes in my saws. I do store gas in those machines, with stabilizer, for no more than 3 months during their use seasons, but I turn off their tanks and run the lines and carbs dry just as I do with the saws. Since these are 4-cycle engines, I can drain their tanks and put the gas in my truck at the 3-month point. All these engines start right up on regular gas. I tried higher grades, but saw no difference in performace, so I save the extra money for a better grade of beer 😀
Simple way to approach this is to not store gas in your chainsaw, and try to mix only what you'll use.
Hope this helps.
mm