Back when I was trapping, I believed that the Connibears would be likely to break ribs and puncture skin, reducing the value of the pelt. We did use them here and there, mostly in streams for mink, and that never happened.
The Connibears have to be set vertically, so that the animal can run through them. In Cold Bay, there weren't a lot of places we could do that, and that may be why we never overcame our prejudice against them.
One big advantage of leghold traps is that if you trap something you don't want, you can let it go.
I'd advise you to have some of each; they each have some strong points.
Nels