Two home insurance policies - one bought by society and second one myself

[Rahul]

I am living in a society flat. I hold two home insurance policies - one bought by society and second one myself. Both are from m two different insurance companies (ICICI Lombard and Bajaj Allianz, respectively).
1- Which one to keep and which one to cancel, please advice?

First check the coverage available to the society policy, mostly society policy only have cover of Fire and Special Peril Policy with earth quake rider.
Second - You cannot cancel society policy.

2- Whom should I call in claim?

You can call both the insurer.