I saw a 6200 mAh battery on ebay for about $10, so cheap so I gave it a try. It works, but later I found the claimed capacity is far less than 6200, not even close to 5200 that its volume suggests. After fully charged, its level drops below 90% in 10 minutes or so. The seller sent me a replacement, but it behaves exactly the same. I returned them for a refund.
I do need a high capacity battery for my S4, as I'm preparing for a long trip soon when I need my S4 as a mobile hotspot for my laptop (the Miix 2 8). After some search, the Anker 5200 gained good reviews on Amazon and it costs only about $20. I bought one, it is real and an excellent product.
Very well packed, sealed, film protected and even well documented, far exceeding my expectation from such a low price and a company that's not a big name:
It's heavier than the fake one:
I'm glad I found Anker, it'll be my choice for batteries from now on.