600D is for around 71k which also leaves u space for getting additional and better lenses.
And the Nikon vs. Canon part it is just another war like Corolla vs Civic, but i would recommend that you once visit the outlet, and use them, feel their grip and also check the ease of use and what easily adjusts to you and then buy that Brand. Everyone would recommend you buy the brand they like but its better you compare them online atleast (not required though, they are the same) and DO go once at the outlet and personally check them BOTH out.
Overall
600D>D5100 - Video, Wireless Flash Control, Cheaper lenses
D5100>600D - Picture Quality, Better High ISO results, Faster Burst shots
in addition, do check this link:
Canon-600d-vs-Nikon-D5100 
My recommendation: Nikon D5100 
as you already have 100k to spend and if u buy the D5100 you are left with enough cash to get the best starting line-up of lenses, so you may ignore the 'cheap lenses' matter ONLY in YOUR case 