I don't think it's really fair to compare the D3200 to the T3i since the T3i came out more than a year earlier. Or, coming at it the other way, I think it's more fair to compare the D3200 to the T4i which came out around the same time. To wit:
Gordon's high ISO comparison of the T4i vs D3200 is here
. (Also, for static shots, note the T4i's Multi-shot Noise Reduction mode at the end of the page.)
(Also, for the sake of completeness, Canon just released the T5i. There's a preview thread in the Canon section of the forum
And the T4i is better for video:
- With an STM lens, video auto-focus is quieter and smoother.
- You can "pull focus" via the touch screen on the T4i. (There's the demo video of this feature on the first page of Gordon's review.)
- Live Histogram.
- (The T4i has an external mic jack.)
- (You can adjust aperture while shooting video on the T4i.)
Lastly, although both Canon and Nikon have comparable lenses, for indoor/night sports, be prepared for things to get pricey.
Full disclosure: I own a T4i (and shoot video with it) - Mark