It is better to have a large bandgap, as this allows for absorption of higher energy photons, and generates a large voltage in the PV cell.

It is better to have a smaller bandgap as then more electrons can be absorbed, and the alpha factor will be higher, meaning less material is required

The best option is to be part way between, so that the voltage can be high, the losses can be low, and the alpha factor isn't too bad.