Base on the premise that all the conditions are the same, if the drive circuit provides enough voltage, the speaker can generate higher sound pressure level. However, with the same voltage, but we use another speaker which applies higher rated power, it will be difficult to drive and output lower sound pressure level.
For example, a circuit can only provide the power of 8 ohm 1 W, in order to generate higher sound pressure level we collocate a 2W speaker, the SPL will be lower instead of higher. It is because with the increasing of the power, the diaphragm should be thickened. The coil also needs to be replaced by thicker wires. However, the thicker wires results in lower impedance so we have to wind a bit longer more, and that makes the coil heavier than before. Oppositely, if we use another speaker which loads lower power or with lower impedance, it is likely to make a little bit higher SPL, however the noise or burning down will possibly happen in this condition.