If it's a carburated motor I can't think of "what extra value" the cost difference would give you.
You are still mixing at 50:1 (or if your motor has a variable oiler, at whatever rate it mixes at) - so not giving you "extra mileage".
Traditional 2 strokes are already inefficient (as opposed to new direct injected models) - so you have lot's of unburnt oil/gas going out the exhaust - if it's synthetic that just means you are paying two or three times more for what you aren't using (along with what you are using).
Two strokes get damaged by a lack of oil. That is almost never the "oils fault" - if you have a clogged carb in a multi-carb set-up so that no mixed fuel is getting to say #2 cylinder, it doesn't matter "what oil" didn't get there.
Now if you are running an injected motor there has been much discussion about, minimally, a semi-synthetic being easier on the injectors and if you have a direct-injected 2 stroke, most mfg's insist that you must run fully synthetic, but the regular old carb'd 2 strokes were designed to run on regular old dino-oil and there is hundreds out there that are 30 or 40 years old which kinda tells me that you don't need anything fancier for their longevity.
I don't know if synthetic is anymore (eco-friendly) and if you lean that way then maybe it's a reason to use it, but the newest of my 4, well used outboards is a 1991 model and none of them have ever had any issue using dino-oil or 10% ethanol fuel (ran them on E-15 for two years when one of our stations was test selling the stuff - so ran it "just to see").
So "for me", if the mfg say dino-oil is fine, I tend to believe them and unless a product that costs two or three times more lasts two or three times longer, or makes it run better/stronger/faster (at which point I have to judge if the improvement warrants the extra cost), I just stick with what works...