I've had many fine speakers over the years & while there are no hard & fast rules regarding music reproduction, I think that generally high efficiency speakers sound more like live music than lower ones. Its not just a simple matter of more watts to compensate for lower efficiency. The dynamics & transient response for myself are what differentiate good sounding "hifi" systems to ones that actually can sound like live music. I've heard a few, very expensive lower efficiency speakers driven by very expensive heroic, 100 lb. + , 2 + foot long amps that can do this but you can buy one very nice, very fast Ferrari or McLaren for that kind of money (w/ a decent sounding stereo system...) of two or three pretty nice German, decked out sedans (also w/ good sound systems - for a car). Crazy $$ for a few lucky folks.
Of course, as others mentioned to get good bass that can play loudly & high efficiency, he need to have a large speaker w/ a large woofer or two which can also be somewhat pricey. Along w/ that can come some limitations at the frequency extremes & coloration, especially from some horn loaded speakers. I think there is a trend today to connect multiple smaller woofers in parallel to gain efficiency at the expense of reasonable impedance loads which can cause undue strain on less than very good amps & thus potential distortion.
I found & now own what I consider to be an excellent balance between all these factors, the Volti Audio Rivals. They're made in TN, "reasonably "priced (about $15K), substantial but not crazy large & sound excellent. They're horn loaded midrange & tweeter w/ a 15" paper cone ported woofer. They're very dynamic, big sound but also quick & detailed, image well w/ very solid bass although not "bat frequency extended" on the high end. They can fill a large room w/ very good sound like few other speakers can at anywhere near their price range. With a good tube amp, they sound like live music & are tons of fun!