Battery life is good, it depends on what you're doing and if you need wifi/3g4g, but I'm pretty happy overall. Battery is removable, so you can always replace it with a new one. One complaint people have is charging is a bit slow, the charger that comes with the phone is garbage but it still takes several hours to charge. Since I charge at night, it's not an issue for me.
Performance wise, it's pretty much on par with the snapdragon 800 series so yes it's pretty fast. I don't game at all, but the GPU is the most recent GPU from ARM so it's pretty efficient.
Camera is pretty decent as well.
Build quality is excellent, it feels like a solid block in your hands. It's made out of plastic, probably not as premium as a Samsung Galaxy S, but I don't think it's a cheap feel either. Somewhere in the middle, IMO.
Phone comes with some useful features - double tap to wake, write a letter to open an app - that I've come to appreciate.
Some of the drawbacks are lack of accessories (there are some covers and cases, but not a lot compared to a Galaxy and you'll probably have to order from China) and lack of open source code (Mediatek won't allow it). The phone is rumored to get Lollipop in the next couple of months, but I wouldn't expect anything beyond that.
Here's a review with some other information:
http://www.gizchina.com/2015/02/03/jiayu-s3-review/
Bottom line is the specs and quality are great, even better considering the price, but you're not going to get custom kernels and Roms like a Oneplus One or the variety in acessories.
Hope that helps. If you have any other questions, feel free to ask.