The folks over at Machinery Lubrication, a industry recognized publication, can help here.
This first article directly compares Group III mineral "faux" synthetic with Group IV PAO "true" synthetic....
Performance of Base Oils and Future Trends - The Evolution of Base Oil Technology - Part 3
From that first article.....
A modern Group III oil can actually outperform a PAO in several areas important to lubricants, such as additive solubility,
lubricity and antiwear performance. Group III base oils can now rival PAO stocks in pour point, viscosity index and oxidation stability performance.
Polyalphaolefin (PAO) Lubricants Explained
And excerpt from the second article........
Lower natural lubricity than mineral oil
Polyalphaolefin base oil not necessarily less wear than mineral base oil (additive-dependent property)
Compatible with mineral oil
Problems very non-polar (low natural solvency, additive solubility, lower lubricity and film strength)
Forms hard deposits in reciprocating compressors
Must blend in 5 to 20 percent ester base oil for seal swell, additive solubility and lubricity
Not biodegradable
Costs four times more than mineral oil, less than other synthetics
There are some advantages to a PAO. It isn't that Group III exceeds it in every category. Especially thermal resistance. Hence, most of the motor oil I use is a combo of 75% Group III and 25% Group IV.