First, the Sony SLT A55 has been discontinued and replaced by the SLT A57. You can probably find new A55 cameras at close-out prices though.
The Canon 600D/T3i does not allow for auto focus during video. The Sony SLT A57 with Sony's Translucent Mirror Technology allows full-time, continuous phase-detect auto focus whether you're shooting still images or full 1080p HD video.
The Canon 650D/T4i when fitted with the 18-135mm f3.5-5.6 IS STM zoom lens allows for auto focus during video.
Don't be misled by anyone claiming that the Sony lens selection is lacking. What they aren't telling you is that the A37, A55, A57, A65, A77 and A99 all use the legacy Minolta Maxxum "A" lens mount introduced in 1985. There is still a good supply of previously owned Minolta Maxxum AF lenses available and all of them are compatible with the Sony SLT cameras.
If your budget allows, I suggest looking at the Sony SLT A65 which has a much faster OLED (Organic Light Emitting Diode) electronic viewfinder. The A65 was chosen by the Technical Image Press Association (TIPA) as their 2012 "Top DSLR Advanced".
Prices from B&H:
Sony SLT A57 w/18-55mm zoom, $598.00 after a $200.00 'Instant Savings' from B&H that ends 03-02-2013.
Canon 600D/T3i w/18-55mm zoom, $699.00.
Sony SLT A65 w/18-55mm zoom, $798.00 after a $200.00 'Instant Savings'
from B&H that ends 03-02-2013.
Canon 650D/T4i w/18-135mm STM zoom, $999.00 after a $150.00 'Instant Savings' from B&H that ends 03-02-2013.
B&H - http://www.bhphotovideo.com
Reviews:
Sony A57: http://www.imaging-resource.com/PRODS/sony-a57/sony-a57A.HTM
Canon 600D/T3i: http://www.imaging-resource.com/PRODS/T3I/T3IA.HTM
Sony A67: http://www.imaging-resource.com/PRODS/AA65/AA65A.HTM
Canon 650D/T4i: http://www.imaging-resource.com/PRODS/canon-t4i/canon-t4iA.HTM
My suggestion is the Sony SLT A65.