Sony HX50V OR Canon SX510 - Purchase decision

[craige4u]

I am looking for a camera that has great image quality and the camera that are within my budget are:
Sony HX50V, Canon SX510 and Nikon P7800

Now, right during the demo in the shop 2 diff. Nikon camera produced "Lens Error" and camera stucked and moreover the shopkeeper himself agreed that even his Nikon camera is having Lens Error problem every now & then..... So I really wonder does the Nikon quality really went so downhill ?

So, I guess if I wana play safe I am left with the next two option - HX50 and SX510.

1] Please inform me which camera would be great for taking normal holiday pictures that are crisp, clear and capable of cropping properly via photoshop.
2] What movie mode is superior for normal movie taking 24FPS (Canon) OR 60FPS (Sony) ? I seen sum samples of Sony and strangely it has sum stutters when the user pans the camera even slowly.
3] Which of the two, will keep auto refocusing in movie mode when the scene changes?
4] I like sumthing that I can hold in my hand via wriststrap and cannon is slightly elongated and I don't wana use big pouches so whts the alternative to carry it around effortlessly without a bag.

Do provide your inputs.