Thanks! So when it comes to video quality, a GH3, a Canon 50D, or a Nikon D5200?
I would go for the GH3. The Canon 50D does not do video as far as I know unless you mean the 5D MkII or MkIII and I still think the GH3 with its 50Mbps bitrate will deliver better video. I don't know much about the Nikon D5200 except that until recent models you could not change aperture (in Manual mode) without exiting Live View.
With the Canon's and the Panasonic Lumix GH series you can set aperture, shutter, and ISO independent of each other in Manual video mode. This is important if you want full control over exposure. Here's how I do it:
I set shutter to 1/60th (I'm in NTSC "territory" and this sync's shutter speed with power line 60Hz freq to prevent flicker and banding if artificial lighting is in the scene. In PAL regions this would best be 1/50th), ISO to where I think I want to try it, and aperture for depth of field effect wanted. I may "tune" exposure with ISO adjustment or I may use ND filtration to get the aperture more where I want it (Outdoors in bright daylight/sunlight you don't want to be stuck with smallest apertures on the lens, diffraction effect can cause loss of contrast and sharpness).
The cameras I've used always had a meter readout at the bottom of the screen, a histogram if wanted (it's not an exposure meter but can help if you know how to interpret the display), and the GH3 has an EVF which helps you to prevue actual exposure effect. The LCDs on the back of the various cameras are of extremely limited value in trying to visually judge exposure unless a "loupe" is used on the back of the camera.
Of the three cameras you listed, the GH3 is the far better film making tool hands down. I've worked with the Canon 7D, T2i, T3i, and 60D; all got me good results but when I switched to Panasonic GH2s, then GH3s, and now the GH4 being able to see more what the video was going to look like in the viewfinder is something I appreciate!
Hope this info helps