For photos, it's not as much the camera as it is the lens. You really need one with an f-stop of 2.8 or better to handle the low lighting on the venues and the the quick action, nut these lenses can be very expensive.
For video, I have a JVC enverio. Takes great HD videos but o am not fond of the screen. The touch screen is not sensitive enough to touch and there are no other controls so you have to use it. Also, it is very hard to see the image on the screen in sunlight. I mainly use it indoors but at baseball games, its horrible. I had to by a viewer cover to cut the glare. But it takes great video so I am mainly happy with it. Stills from video are ok. I went with it because it is on the less expensive end for the HD quality, which is what I really wanted.