Rich,
I disagree. I think the critters do care. Maybe it depends on what you are calling for, but anyone who has read much of my junk knows that I am primarily interested in cats. Coyotes are way down on the list somewhere.
I know for a fact that I have personally called in far more cats using a call with a clear, high pitched scream, as opposed to a low, gravely, jack rabbit type call. I have several of what are commonly referred to as "jack rabbit" calls. They are pretty much at home in a cigar box. The calls in my back pack are open reed calls, and I prefer to tune them myself.