The store I went suggested me to upgrade to Sonya6000 and buy a sony Lens for birding.I have read about the 11fps and AF tracking of the a6000. I can sell my NEX6 for around 500$.
My question is will a6000 be a good body for BIF and wildlife photography ?
First answer is: Yes. The A6000 body, and all its developments in focus ability, is an excellent tool for wildlife and birding - the focus is immensely fast, very accurate, it has very good controls with excellent customization, and it's one of the first mirrorless cameras with a large sensor that can legitimately focus continuously on a moving subject as well as a DSLR.
Second answer is: No. Why? Well if you need a good diversity of lenses that fully autofocus, or are stabilized, the e-mount system currently does not go past 210mm. So the reach is not very good for most birding needs for most people. There are ways to extend that reach with extenders and adapters, however this might only work in certain locations where light is abundant.
DSLR lenses can be used on the e-mount cameras, via adapters - some of these adapters would allow use of Alpha lenses at the same general speed and functionality of Sony's SLT models, since they actually use an SLT mirror and PDAF array right in the adapter...other adapters would have slower autofocus, or none at all.
Third answer is: It Depends. Why? There's a mighty big difference between birding and wildlife shooting in northern Minnesota, South Florida, and the fens of England. How close can you get to the wildlife? How is the light and weather where you are? Will you be shooting lots of moving wildlife and birds, or more still ones? The limitations of the A6000 are purely in the lens department - for ME, I can use an A6000 to very good effect, because I live in S. Florida. Slower lenses don't worry me because I have oodles of light down here. 200mm limitations don't matter as much for me because I can get within a few feet of birds and animals. Adapters can extend my lens reach to 350-400mm, which works OK down here with slow aperture lenses. If you live in grey,overcast places with lower, poorer light, or are trying to photograph animals that won't let you get within a football field's length of them, then it won't be your best system for this type of photography.
If I use Canon or Nikor lenses on Sony a6000..with adapter..would there be a performance loss?
Yes - no autofocus, or with expensive adapters, very slow autofocus. You'd want to stick to primarily e-mount Sony lenses, or Sony Alpha lenses with the LA-EA2 adapter as your only reasonable choices for any moving or fleeting birds or wildlife.
I use a DSLR and an A6000 for birding - both are excellent. But my caveat on the A6000 is that you would need to live in a similar place as I, where you can get closer to wildlife and won't have as much of a concern over lack of long-reach lenses.