The FX-8350 was released at the beginning of 2012, and is extremely old, but it has aged pretty well. It's similar to a Core i3 in most games but draws about 3x as much power. It may or may not work with a 970 board, depending on whether or not the board supports 125w CPUs. Many are limited to 95w chips and using a higher wattage chip will result in bluescreens and possible damage to the board. Which board exactly?
The A10-7870K is closer to a Pentium dual core in overall performance (~$50), and is only as expensive as it is because it includes a relatively large integrated GPU. This GPU unfortunately is still only barely adequate for running higher budget games at minimum settings with barely playable framerates. This chip uses a different socket.
Most people recommend strongly against either CPU. Both perform worse than similarly priced Intel chips, but if you're just looking to build an AMD machine and you don't really care about how well it performs or if it's a good value, the FX is a better choice despite being older. However, AMD is set to finally release a new high-end CPU design for the first time in 5 years in about 3 months and will probably be discontinuing both of the CPUs you listed, so if you can hold off and see how this new line of chips performs, I'd recommend that.