I can't really give a solid answer as to whether you will see the benefit unlesss I know what resolution you play at. If you only play at 1600x900, then you would never see the benefit as most games can be maxed out by a 670 at that resolution because the refresh rate of 60hz would never be able to show anything higher than 60 fps. ALso, If you only play older or less demanding titles, you really won't see much of a benefit as a 670 is still a very capable card. While the 970 is a much faster card, I would need more information to tell you whether you would see the performance benefits.
I mean, As I see it, Both a rifle and a bazooka will kill a dear. The only question is, Why would you need an overpriced bazooka to do a job that a much cheaper rifle could do? I suppose that it just depends on your needs so to speak. But, I would just try to save money where you can. You could probably sell your 670 for about $200 on Ebay and then use that money towards a new 970 if that floats your boat, so to speak.