Not working is rare. I have run into this twice and it was a BIOS or motherboard issue. It's very rare. The issue more often is the owner struggling with drivers.
As to comparing, Here's a few links to compare the 580 and 970 and the new 1070 vs the 970.
The thing is, the 970 is a really good card for 1080p 60hz play. I would not change this card yet.
970 vs 580 link:
My view. A small step up. But not enough for me to do that.
970 vs 1070ti link:
Great step up but you are paying for that.
At the end your choice. HOWEVER did you move up to SSD yet? It may give your PC a whole new feel without going over 200 bucks.
So I'm currently running a GTX 970 and i feel like it's aging. Probably need an upgrade. I'm also not trying to make my bank account cry. And im newish to computer building. My question is this.
A) Sense in running an Nvidia card can i even install an AMD or will that not work?
B) Is a Radeon 580 a good upgrade from the GTX 970 or would it be pointless and i should spend the money on a 1070ti.