Although it is good practice to adjust loudspeakers being compared to be at the same loudness level, it is an inherently flawed process because loudspeakers can have quite different frequency responses. So, the precision of the loudness match is best for the better - more neutral, more similar sounding - loudspeakers.
Does it matter? It depends. In the early days of my research I did comparison tests with matched and unmatched loudness. Back then many loudspeakers had clearly audible resonances, and these loudspeakers were identified and downgraded even with mismatched loudness. The more neutral the loudspeaker the more critical the loudness match, and here the dominant factor is subjective loudness - described by the equal-loudness contours. This means that differences in overall sound level are perceived as differences in bass balance. Since bass accounts for about 30% of our overall sound quality ratings, such differences have a magnified influence. Speakers having different low-frequency extension are especially influenced.
Otherwise, the vast majority of loudspeakers are so well designed that non-linear distortion and power compression are not issues unless the products are driven to extremely high sound levels - at which point the non-linearities of our hearing gets into the act.
In summary - sensitivity, per se, is not a factor unless the power amps are driven beyond their linear and stable current and voltage ranges for speakers with low sensitivity and/or low impedance - which happens. See Part 3 of the Designing a Home Theater series on the companion website for the 3rd edition of my book: www.routledge.com/cw/toole
. Click on the title at the top of the webpage and download. It is open access, no need to buy the book.
A final comment, speakers with very high sensitivities tend to be horn loaded. These exhibit very different (narrower) directivity compared to cones and domes. This alone can account for significant differences in speaker/room interactions and perceptions.