That has not been my experience. It's true that they are "better at security" in the sense that they know to avoid common security pitfalls like unparamaterized SQL, but essentially none of them have the ability to apply their knowledge to identify vulnerabilities in arbitrary systems.
My point is that more experienced programmers are better at security on average, not that they are security experts.
I've found it to be the opposite. Many of them do have the ability to apply their knowledge in that fashion. They're just either not incentivised to do so, or incentivised to not do so.