1. Neethu loves you more than I.

   Here Neethu and I love you.
   But she loves you more than I love you. There are two subjects here – Neethu and I.

2. Neethu loves you more than me.
   Here Neethu loves you and she loves me too.
   Of the two people (i.e., you and me) she loves you more than she loves me. Here there is only one subject – Neethu.

Thus both sentences are correct.