Will the NVIDIA GeForce GTX 860M against Nvidia GeForce GTX 970M make that much of a difference?
Yes, very big difference. GTX 970M is nearly desktop class.
GTX 860M is old architecture. It doesn't have the power efficiency of GTX 970M
Which of them has a better battery life?
The GTX 860M will provide better battery life, due to its lower clock speed . However, GTX 970M provides more power/watt due to its new architecture.
Either way, these GPUs will be automatically disabled when you use your laptop on batteries
(if it ddoesnt, IT SHOULD) So dont be concerned with battery life when it comes to GPU purchase decisions.
Next time append all your queries in one thread. It makes easier for you to look at the responses you require, its also easier for us to reply all your queries from one single thread.... and it keeps the forum clutter free