A popup would be more easy for me. It saves me from having to make another page. This being said, on average, which method does a user prefer more? A popup may be faster, but do users feel it is as secure or fun?
I will suggest you go with popup.
Now take a scenario that you are searching for some product and after spending some time you finally find the product you want to 'Add to cart or buy' and then you click on sign-in button on Amazon and it takes you to a new page. Suddenly, the product you wanted to buy is not in your view. Amazon redirects you to your previous page after login - but that's after login or giving a user a sense of fear that he/she has to look for the product again.
In case of Flipkart (popup) the user stays on the same page while logging in without the fear of losing the page/product.
If you are thinking about security - popup or new page doesn't make much difference if the URL is starting with 'https'