I personally use all mouth calls, simply because that is what my dad taught me to use when I was a kid. I have hunted with friends that use electronic callers but never with much luck as they just let the call play and play and play. To me, a dying animal would never sound like that because they don't have that much air in their lungs. I personally use short softer distress calls about every minute to two minutes in case that coyote is just over the hill. Gradually getting louder the longer I sit but never blowing on the call for more than 10 seconds.
As for what distress sound to use. I go by what animals are readily available in the area where I am hunting. I grew up in Western Nebraska where Jack's and Cottontails were both plentiful so I used both. Here, I have not seen many Jack's so I don't use that call. I believe a coyote can tell the difference in a call and if something doesn't sound normal, they won't come. I also use a woodpecker distress call if I am calling in or closer to heavier timber and it is also my call of choice for bobcats. I have just had better luck with that call than I have with a rabbit in distress call for cats.
I have howler's and pup distress calls but I don't use them much unless a coyote barks at me first because he has seen something he doesn't like or is just unsure. In those instances I just try to mimick what that coyote sounded like to make them come look.
My go to call was a little Primos cottontail distress call but I gave it to a 12 year old kid whose dad allowed my son to shoot his first turkey in Nebraska over Christmas. He was wanting to get started into calling so I went with him and called a couple in for him to shoot at and he had a million questions about the call so I figured he would put it to good use as I don't call as much as I used to. Other than that, I like my Johnny Stewart calls the most. Sorry so long but I hope this helps. Just some things I do.
Gundog