I'd say the winner there was the Mayor. Piers was being a dick on TV; that's his job. He's trying so hard to be a bull-headed talker-over like Chris Matthews or Bill O'Reilly, but he's just a TV dick.
The Sheriff didn't have any facts, he didn't answer the questions, he couldn't think outside of his one talking point. The Mayor, on the other hand, was well-prepared with a good argument for one of the issues out there now that both sides generally agree on - that is, keeping guns out of the hands of violent criminals and the mentally unstable. The Sheriff could have easily said, "Yes, we need that, but until that takes effect - which will be a while - this is what I am saying to the people I serve to help keep them alive."
But he didn't. He strikes me as being kind of butthurt about having to lay off some of his deputies.