Canon Eos Rebel T3i V. S Nikon D3200?

Which is better and why? I mostly will use this camera for taking pictures

Both are mediocre. You have better choices. For dSLRs Canon ranks at the bottom for their image sensor performance across the board, with their crop sensor dSLRs doing the worst (Rebel, 60D, 7D).

Then you have nikon, they use the best image sensors from Sony, but the 24 megapixel sensor is a dog, too many pixels, performance suffers in low light.

Better choices in a similar price range, Nikon d3100, D5100, Sony A37, A57. If I were shooting mostly stills, the best choice would be a Pentax K 30, if shooting lots of video, the A57 would be better.

I would say that the EOS Rebel T3i is slightly better than the D3200 as it has more advanced support for stuff like wireless flash, it can do HSS flash (high shutter speed flash sync at all speeds with a dedicated gun), it has a DOF preview, and mirror lock up, and exposure bracketing.

If you are planning on getting into photography fairly heavily, then the T3i will be a better solution for you.

There's no difference, at least not when you are given an answer by someone who is not loyal to a certain brand. Many people on here will either answer Canon or Nikon solely based on which system they use to take photos. The truth is, both are great entry level cameras with pros and cons. What is important is to pick each one of them up, feel it in your hands, go through the menus, take a few pictures and then decide. One will feel more right to you than the other. Shutter speeds, flash compatibilities, and megapixels aside, the best camera is the one you will use and will use often. Nikon and Canon both make great cameras so whichever one you chose will serve you well if you chose it based on my advice and not loyalists or fanboys of either brand.