If you have the money for the 5960X, it *WILL* help. I'm not gonna deny that. It is going to be harder to clock up though, but in games that are single or dual-thread heavy, you'll be able to force OBS to the latter 8 threads etc, so it overall will work out better.
I'd say if you have the money, PLEASE make sure you know what you're doing with the boards and power supplies etc, and then go for a 5960X. It will definitely be the best thing you could think of for streaming.
And 1080p 60fps "fast" should not be out of reach for some games even. But I would still suggest 720p 60fps, and pouring on as much compression as you can, because not only will it be easier for viewers to decode it, but it will look much better especially in fast motion games or games with similarly coloured, repeating patterns (like DayZ's grass).