Which one of these DSLR cameras should i pick?

Cannon 600D EOS or Nikon D5100

for outdoor photography purpose

Try Nikon D5100. Compared to 600D, 5100 provides better picture quality and has good exposure levels compared to canon for the price available.

If i were you, i would go to a digital store and compare both and conclude.

Both would be fine, unless your definition of "outdoor photography purpose" includes some serious wildlife or high-speed sport captures, in which case I'd suggest a body with higher frame-per-second rate, such as Nikon D7000 or Canon 7D.

Depends what you are shooting and how…

the body is likely to be immaterial… Because any camera can be used in "outdoor photography", but what you are shooting is the important thing…

if you are shooting landscapes, then either the kit lens (18-55mm) will do - or a 10-20mm or 10-24mm for wide angle landscapes…
if you are shooting "wildlife", then something like a 70-300mm or 150-500mm…
if you are just wanting a "blurred background", leave the room now…