The T3i has 17.9 MP, whereas the GH2 15.9 mega pixels. (10% more detail captured). Higher true resolution.
Those numbers are for stills. These cameras all downscale to 1920x1080 pixels for video (if you're lucky), which is equivalent to about 2MP, so maximum sensor resolution is not really relevant for video.
It is the downscaling algorithms and the video processing that are important, and as Andrew Reid from EOSHD said in his
review of the
T3i/
600D back in 2011, "In stills mode the
600D has the edge especially at higher ISOs. But it loses a lot of the advantages of a better sensor, because it’s video image processing is so primitive."
Here is the side-by-side he shot between the
600D and an unhacked
GH2:
http://vimeo.com/22318115
And here are identical films shot on both cameras:
Hacked
GH2:
http://vimeo.com/39955014
T3i/
600D:
http://vimeo.com/39050472
It's pretty clear which camera has the best resolution. But that doesn't always mean "better". Some people like the Canons' softer look. I'm not one of them.
I am not a Canon hater, I started with a
T2i. But I sold it and bought a
GH2 because the
GH2 had almost no moire, a useful crop mode for lossless 2.7x telephoto, a swiveling LCD, video autofocus that actually worked, its viewfinder continued to work when I shot video (Canon DSLR viewfinders go blank in video mode - the mirror blocks them), and it had essentially no video clip length limit (the
T2i,
T3i,
5D Mark II and
7D all stop after 12 minutes of continuous recording and must be restarted).
Canon has slowly fixed these deficiencies - they added the swivel screen and crop mode with the
T3i, they added rudimentary autofocus and extended the max recording time to 20+ minutes with the
T4i (but took the crop mode away), they added the crop mode back in with the
T5i and finally added real autofocus this year with the
70D.
But they still have the moire problem, they are still limited to 30 minutes of continuous recording and they still lose their viewfinders in video mode.
People make beautiful videos with Canon cameras despite these challenges, but for me, dealing with these limitations was too much work and I
stuck with the GH series when it was time to move on from the
GH2.
If you want the best value for your money, and can still find a new or used
GH2, I recommend you snap it up. If you can't find one, or can't afford one, the
T3i is an adequate second choice, as long as you know its limitations going in.
Cheers,
Bill