Your question is really interesting. Firstly I can say that the technique depends on your purpose: if you want to make lots of printings very quickly there's no doubt: screenprinting on frame is the best choice. In contrary, if you have to make just few unique printings, not an exact copy of one another, with lots of shadows the best technique is the airbrush. But in this case you have to pay attention to use a very diluted ink that could loose its coating. With screenprinting you use dense colours with a higher coating.
Preparing a screenprinting frame is expensive but you have to think about of the material of the stencil and so even to how many time you can use it before it will get ruined. I think that you can try both, evaluate the printing results...and let us know!

This is Franco Ratto,