nikon 70-200 vs sigma 70-200

I currently own a d7000 and pair it with the nikon 70-300 vr for shooting animals and planes. I am thinking about upgrading to something better like the 70-200 2.8 with a 2x teleconverter. Anybody here has experience with the nikon and/or sigma combination with the teleconverter? Is it worth the difference in price between the 2? On the 400 side of the range, will I need to shoot handheld and still get decent sharpness?

Thanks.