Are any parts of Panhandle in San Francisco more safe than others?

No, no areas of the Panhandle are more safe or more dangerous than other areas. The park area itself is pretty safe and I think you can see across it all the way through all the way across.

If you are talking about the neighborhood around the Panhanlde, I would say that North of Panhandle is safer the Haight neighborhood on the south, but I'm not sure how much safer really. They aren't that far apart.