The 580 is better but it's not really a massive upgrade, think high settings as opposed to medium at the same fps on modern titles.
Its an awful time to upgrade, everything is overpriced.
There are loads of threads with similar questions at the minute, the general concensus is hang on to what you have and wait for prices and availability to stabilise.
The 580 is only worth upgrading to if you can do it for less than a $50 outlay after selling your 970.