If you do not need the faster processing for high speed photography get the 650D and use the money toward lenses. that is the advice that most people will give you. Really, you can go wrong with the 600D T3i either.
This guy does some great reviews. I used this site and a few others to decide on my T3i over the 60D.
I don't shoot video, so I can't help with that. I was under the impression that the 650D did autofocus during video. If that's important to you then that's pretty much the decision right there.
For photography the 60D has some nice little features. Nothing significant, but they're worth it to some. Really I think the biggest difference is ergonomics, which is a personal choice. The weather sealing is nice, but it's not as big a deal as the internet makes it out to be, IMHO.
Both are good cameras, and not all that different in price. My personal recommendation is tth e 650 and save the cash for lenses, but you can't go wrong with either decision. I will however recommend the 650D over the 600D, as the added cross points are worth the slight cost difference.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM