Long Lens, No Better
With regards to low-light performance, both the Canon and Sony will not do much better than your current camera. While sensors do get a tiny bit better each passing year, the SX50 and HX200 still use a very small sensor and equally small aperture lens. Really, they are just like point-and-shoot compacts, but with very long lenses.
Of the two, I personally would choose the Sony. A 50x zoom is neat, but unusable without a tripod. If you really want better low light performance in a long zoom camera, the one to get is the Panasonic FZ200. The downside to the Panasonic is its high price.