The T3i is a better camera with more features and a better, more modern sensor. The T3 is a budget model which uses older generation technology and leaves out a number of features. Plus the 75-300mm lens isn't very good -- you'd be better off with the 55-250mm IS lens which has IS Image Stabilization useful for fighting blurring.
I would tend to recommend not relying on the internal flash for this kind of thing but instead to consider an external flash like the Canon Speedlite 430EX II. In poor light, the internal flash uses bright pulses of light to provide enough light for the focusing system to work properly but these light pulses can be extremely distracting for your subject. The external flash uses a much less intrusive red focusing beam. Light from the 430EX can also be bounced from a white wall or ceiling in order to create a much softer and much more flattering quality of light. Also, the 430EX recharges much faster for the next shot, has greater range and doesn't eat up your camera's batteries.
For photography I think both are almost the same.
But in the video subjet, the T3i is way better. In the the video mode you can control ISO, Speed, Aperture... In the T3 you can't just auto mode.
If you you want to save some money and just take pictures and video in auto mode. Go for the T3... If money isnt a issue go for the t3i for sure.