For MiniPID 2s with supply voltages between 3.0 and 3.6 V the internal rail voltage will be the same as the supply voltage. This means that a higher rail voltage will increase the brightness of the lamp and therefore increase sensitivity. A lamp will be approximately twice as bright running at 3.6 V compared to running at 3.0 V.
MiniPID 2s with supply voltages above 3.6 V have an internal voltage regulator. This means the internal rail voltage is kept at a constant 3.3 V irrespective of the supply voltage, and therefore the lamp brightness is kept constant too.