The only measurements that I find of any value is the impedance the phase angle. A flat impedance curve with minimal phase shift makes for a very easy load, opening up all kind of opportunities with amplification (think single ended triods for example). A impedance curve that has lots of low drops and especially when combined with significant phase shift is much more difficult and requires an amp that can handle this (think old Krell or current Gryphon amps).
Then the sensitive comes into play. A very easy load with high sensitive (Zu Audio for example) makes it a perfect match to low power amps and as a matter of fact (and personal experience) might not work well with a high power amp (in my case, the volume control of the integrated amp was simply too sensitive to either it was too loud and one click lower and it wasn't loud enough). Low sensitive combined with a difficult load and you will need a monster of an amp with lots of power, but even more so lots of current.