I'd go with the Xeon X5687, the higher clockspeed will make a difference in gaming more than the extra cores or threads of the X5690. Your current Xeons are slow, due in part to being lower power demanding CPUs. The X5687 will be using a lot more power.
One thing I'd do before I spent money on this is to make sure either a X5687 or X5690 can give you the kind of framerate you're looking for with a 970 class videocard. There's no point of buying the fastest CPU your motherboard can handle if it still won't be enough. Ditching it for something new as in 'brand new'? That would be expensive right now but if you have the money then yes, brand new would be better. You could also buy used, maybe move all you components to an Ivy Bridge/Haswell based system. It would be better than what you have, work well with your 970, and not cost as much as an all new system. The downside is you'd be sinking more money into outdated tech and it's used, so reliability might be questionable.