Impedance is how much resistance the speaker produces, sensitivity is how loud it gets given a certain amount of power. You could also think of sensitivity as efficiency.

Oversimplifying the math to illustrate this point - A headphone with a sensitivity rating of 75db will be about 75% as loud as a headphone with a sensitivity rating of 100db when connected to the same source.

A higher impedance headphone will typically sound worse, but not necessarily quieter (though often it's inherently quieter too), than a lower impedance headphone when connected to an amp that's not powerful enough to drive it. Think worse bass extension, less clarity. It still makes the noises it's supposed to but the amp is really struggling to control everything in the tight manner it's supposed to. The voice coil is also frequently able to generate a larger magnetic field from the higher impedance design, so if you've got enough power to drive it properly you COULD get better sound out of the higher impedance driver all other things being equal. The thing is they're never equal which is why there's not a "right" approach here, just tradeoffs to be made given what you're trying to accomplish.