SX50 HS vs DMC-FX200 vs DSC-HX200V

Looking to replace an 18 month old Panasonic DMC-ZS10 (which replaced a ZS7 from Late 2010 that got dropped) that honestly I was never super happy with. It did OK outdoors, but indoors, low light, almost anything with a flash was so-so at best (although I'll admit my Photog skills are probably less than so-so also, so the camera isn't all to blame).
Looking for something in a "Super Zoom" category that will be a decent replacement with the understanding that the 3 I listed in the Title are not going in my pocket like the ZS10 did, although it was on the top end of what I consider "pocket-able" anyhow.
Have 2 younger kids, they do sports that we like to photo, normal around the house family stuff, we travel a bit so want something that will be good for both indoor and outdoor. Going to Washington DC/PHI/NYC next year, so need something new before then.
Looking at the Canon SX50 HS vs Panasonic DMC-FX200 vs Sony DSC-HX200V. With both the Sony and the Canon at or just under $400 and the Panasonic right at $500. I like the idea of the 50x zoom of the Canon, but it appears that the Panasonic and the Sony have better Flash and with the 2.8 Aperture the others might perform better in lower light/indoor situations as well.
We do some video with the Camera as it's generally better than my phone, so the 60fps 1080p for the Pana and the Sony are also pluses. The Sony having the GPS is nice, and even though I had it turned on all the time on my ZS10, not a make or break feature.
Size and weight wise, all 3 are pretty similar from the specs...
Thoughts on these 3? Is the Pana worth the 25% premium over the Sony and am I missing something on the Sony? The only other one in the same general area that I could see is the Nikon Coolpix P510. Slightly cheaper and closer to the Canon I think!
Thanks in advance for your sager advice and comments!
SW2