The advantage (all things being equal however...i.e, quality attempts at speaker designs here!!!) of higher sensitivity speakers overall, is that they usually have a much better dynamic efficiency and "snap" to em than lower counterparts!!! Super efficient horn designs (just go to any THX certified cinema where they use Horn speakers and listen!!!), like Avantegardes at 100db sensitivity and such, are way way dynamic and effortless sounding!...the dynamics just slap you in the chest with authority!..even with low powered amps driving em!...just more efficient and sensitive overall! The lower sensitivity speakers ask a whole lot more out of an amp for similar results!...but at that point, your already running out of the limits (and steam) for the drivers on the lower sensitivity speakers for the same volume or out put! For instance...the 87 db sensitive speakers, is running 3 time harder to try to match the volume of what a 93db sensitive speaker is trying to achieve!!! There's so much more head room and "acceleration" left in the 93 db speaker, that it's just effortlessly not hardly even working with much effort!...that's why it sound more powerfull and effortless dynamically overall than the lower 87db designs, and so forth...
Anyway, Unless your talking about "powered" or "active" speakers, which are more efficient as well, in that their amps are more efficient when they are dirrectly on top of the drives of a speaker, driving them dirrectly, your alway's going to get more dynamic finness and effortlessness out of a more sensitive design! Oveall however, you must look at the quality of the gear, and your system your running! If your running the speakers in a pre/pro set-up, using a subwoofer and thus bi-amping your system (say with lower sensitivity speakers), then it's effectively more sensitive than otherwise would be the case with only your mains running!...so it could depend. But, on their own, a more sesitive speaker simply has a dynamic advantage over a lesser sensitivity design!...