In general mixing is improved by energy input. In a STR input comes from stirring and gas input. In a vortex fermentor the gas input comes from the system by stirring, so I assume its input does not count. However, gas entering the stirrer reduces the power input by stirring.
The dependency on power input is small (power 1/3).
In STR's tangential circulation is reduced by baffles to improve mixing by turbulence rather than by the circulation that is less effective to create turbulence. But inserts have a negative effect on the gas sucking, which however might be compensated by increasing the stirrer power input.
I could not reach the paper mentioned above, just the abstract, but that promised evaluated data that may be interesting. Also you could have a look at our general