EBay sellers lie about battery capacity. It's like a law of nature.
The fact is, Samsung and the other big names use top quality battery cells. As there haven't been leaps in the technology since the N3 was released, anyone claiming more power in the same space is full of it. If you want more capacity, you need to let your phone get thicker. If you're willing to do that, the ZeroLemon is in stock with an Otterbox style case. Their Note2 battery is top quality, and gets the capacity they claim. Same with some of the others I've heard about people testing. I see no reason the N3 version wouldn't, and just ordered one myself. The phone ends up about 2x thicker, but with 3x the battery life and a nice case to go with it.