I have no experience with 100LL, race gas, or even "high" octane gas at all. But I do have to say that here in S Ca if I don't run my 2 cycles dry at the end of a usage...I will have carb problems once I try to re-start. My truck, and other 4 cycles, seem to be able to get through the off sessions. Although my truck is run almost daily and for my portable generator I have a valve set-up in my gas line to drain the tank once I'm through using it at that time.
It might sit unused for "months" and I dare not let ethanol gas sit in the tank because it "will" gum up the carbonator!! BTDT too often to bother with messing around any longer. I have found that the best way to avoid carb tinkering is just run "em dry and put 'em away. Sure it may dry gaskets some, but it absolutely doesn't gum up any more carbs! I like to be able to grab a machine when needed, put in fuel, pull the rope and do my work -- without having to take apart a carburetor, massage the engine, then an hour or two later get my task done. I use stabil. seafoam, marvel mystery oil, and blind luck to no noticeable results. After reading all the above comments I can't say that high octane gas is hurtful or helpful...but I believe I'll stay with my methods for now.
MossRoad you make good points but sometimes it just doesn't matter - a 5 to 10 minute chainsaw job turns into hours of frustration and tinkering. Perhaps (almost certainly) your gas is processed differently than ours or others and your methods work for you. They don't for me. Just saying a different perspective on this issue is always available and worthy of thinking about.