The Redmi Note 3 is the best phone under Rs. 15000 available right now.
The nearest competition is the LeTv Le 1S, which is similarly priced.
Performance on both the phones is very similar, with the camera being slightly better on the Le 1S, but multitasking and Gaming is better on the Note 3.
One major reason for buying the Note 3 over the Le 1S, would be the insane battery life. The Redmi Note 3 comes with a massive 4050 mAh battery which can easily last you about 2 days ( on moderate use) with an On Screen Time of about 6.5 hrs.
So, if battery life is your primary concern, then you should go for the Redmi Note 3.
PS: I recommend getting the 3GB RAM model, because it comes with a bigger storage, and who doesn’t love more RAM. If you are planning to use your device for a long time, then that extra storage might come I’m handy.
Hope this helps.