Can you please let us know what you plan to shoot?
Both Nikon D5100 and Canon 600D are cabable cameras. Nikon has advantage over Canon in high ISO performance. However Canon has some cheap entry level lenses like 50mm f/1.8 and 55-250mm. I would suggest go to a shop, hold both cameras in hand, take some sample shots and take one which feels right.
If you still haven't made up your mind, let me try to tilt you towards Canon. There are some great entry level lenses for Canon, the Nikon equivalent of which costs more. The 50 mm 1.8 prime and 55-250 mm zoom are two very popular entry level lenses that people buy besides the kit lens. You can get them both for around 18K.
Entry level Canon bodies also have inbuilt auto focus motor. So in the unlikely case you find an old Canon lens which does not have an inbuilt motor, it will auto focus fine on your 600D. The entry level Nikons (D5100 included) does not have an in body autofocus motor. This is not a big advantage per se, but it might come in handy. I own a 550D, and I personally chose Canon because I felt the Canon interface was cleaner than the Nikon, and I had a slight brand bias towards Canon.
No Canon (eos) body have inbuilt motor. Only some Nikon's have it its an old feature of cams.
Canon 600D has the auto focus motor.
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