Achieving a speakers max potential

Can someone help me better understand the relationship between the amount of watts driving a loudspeaker and reaching that speakers maximum potential? If for example a speaker's power handling range is 25 to 150 watts, will you not reach the speaker's full capability if it's not seeing 150 watts behind it? Will you hear more detail and information out of that speaker if it's being driven at 140 to 150 watts than if it was being driving at say 60 watts at the same volume (dB) assuming of course the amp or receiver and speaker wire are of high end audio quality? I tried to find a thread on this but nothing turned up. Thanks much.