Well it depends on how you define "better oil" and "optimized additives".
PAO should have better oxidative stability than the average Grp III, but after optimizing the additives that difference may disappear. The Grp III formulator's optimized additive package may include more anti-oxidants, that is, optimized to his targets and accounting for the lower oxidative stability of the Grp III. If identical additive packages were added to both base oils, then potentially different additive responses from the two chemistries may blur the differences.
This is all interesting but to a great degree academic discussion since both PAO and Grp III are both overkill for the vast majority of engines, driving conditions, and OCIs. And most of the additive packages are different and designed for each company’s specific technical and marketing targets. In my mind the additives are so powerful of a factor that the small oxidation differences between PAO and Grp III pale by comparison. In theory, with all variables controlled, PAO should give a slightly more stable oil than Grp III, but remember I can make a Grp I oil capable of providing clean engines and extended OCIs, and a Grp IV/V oil that would seize your engine in minutes. That's the importance of the additive system, especially at high temperatures and loads.
If your definition of better oil relates to low temperature performance or volatility, then the differences between the base oils is more apparent and less additive dependent, with PAO having the advantage. But again overkill or irrelevant for most drivers.
Unfortunately it is very hard to define better synthetic oils scientifically. The API engine tests are designed as pass/fail tests for Grp I/II based oils and don’t really show the advantages of synthetics. One can run the engine tests for double or triple sequence to make them more severe, but then these are not standardized tests and what do you compare the results to? UOA is helpful, especially in finding major faults or trends, but there are so many variables such as driving conditions, weather, engine condition, driving style, make-up oil, dust, loads, etc. that you would likely need hundreds of UOAs to draw statistically significant comparisons between two oils.
Personally I define better oils as ones formulated and produced by companies skilled in the art and bent on making the best they can. Top quality and expensive base oils are a clue to the company’s formulating philosophy, but not necessarily the key to best performance in my car.
Tom