Tough one. When people generally say 'best for gaming' they're usually only talking about speed, and the 960BF is quicker than the 970P. You also mention high quality though, and the 970P is the higher quality monitor, hence the price.
960BF is TN Film, 970P is PVA, both use overdrive. 970P is a true colour 24 bit panel giving great colour accuracy and the best black depths you will find on an LCD. It also has better viewing angles. But it's slower than the 960BF.
I'd say you need to think about what your priorities are from the various specs - speed, viewing angles, black depth, colour accuracy, price, looks etc and hopefully that will lead you to the right choice.
You should also be considering the Viewsonic VP930 (MVA panel), which is a quality screen like the 970P, but is generally thought to have more effective overdrive, which makes it quicker.