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I would go with the t3i and save some money. They're almost exactly the same. And to answer your original question yes. The t series is popular for a reason.
T3i or SL1. Save the cash for a good lens. The upper level cameras have better sensors for taking photos in stuff like low light environments, but video quality doesn't drastically change between revisions.
T3i's are dope, and glass makes all the difference. But the t4i is a little better if you ask me. The auto focus is betterm, and the touchscreen is nice. But not that much better than the t3i that you should get it instead.
Also take into consideration with the touchscreen you'll have to take your mittens/gloves off. Not as desirable for filming skiing which I assume you'll be doing.