Higher sensitivity is better as long as its not achieved by simply paralleling drivers, resulting in a lower impedance.
Lower impedance causes amplifiers regardless of type, to make more distortion.
If the speaker is low sensitivity, one common result is something called 'thermal compression' where the voice coils heat up with things like bass notes, causing the driver to be less efficient. This is quite audible and is why people with horn speakers often talk about how much more dynamic they are.