On the basis of customer satisfaction only, Amazon is far ahead of Flipkart at least in India.
If you search Quora for a Flipkart vs. Amazon, you will be amazed by the reviews (most favour Amazon).
This is just one: https://www.quora.com/Is-Flipkart-better-than-Amazon-in-Indi...
There are many more such questions on Quora. I've read a lot of reviews and this was the result: Amazon is more responsive to complaints, returns, usually cheaper and satisfying the customer. Flipkart is doing way worse than Amazon in these departments. There are even a few answers about how Flipkart delivered the wrong product.