Not to say a 1060 is anything like as fast as an (old) Titan X but it's worth looking at EG/DF's quick piece on this era hardware.
I'm happy to say my i5-2500K is good to go and I'm at least waiting to see what AMD do with Zen (release date: like real early 2017, realistically for actual volume shipments - maybe we get some previews of final hardware before year-end but you're not going to be buying anything until after CES) and it can basically provide very little throttling to my OC GTX1070.
But I'm also running to so that even when all four cores are fully-loaded it runs at 4.4GHz and I've got 24GB of fast DDR3 in there. Both the OC and the fast RAM mean I'm not worried. It sounds like you're both using RAM clocked way below modern DDR4 systems (or even fast DDR3) and are stuck at 75% of the clock speed possible from OCing the CPU.
I think it's a bad time to upgrade your CPU because AMD might, for the first time in an age, actually give us a viable gaming alternative to Intel at the sharp end of CPU speeds (but without the Intel price premium for their high end or being forced to buy a chip that's 50% integrated graphics when we've got a GPU already). Zen may actually be basically everything they've promised (if not then AMD will basically tank their reputation and we can welcome a future where Intel is the only x86 manufacturer in town and maybe AMD spins off the ATi team as the only profitable bit of the company avoiding a hostile takeover from any of the other silicon companies who may want to buy up their x86 patents on the cheap*). At which point you'll be able to get a gaming CPU with 8 cores, 16 hardware threads for $400 or less which is equivalent to a modern Intel i5 for gaming but with the extra cores to mean it scales into the roof for everything else (and is future-proofed for when current game engines really go wild with multi-thread designs thanks to DX12 and Vulkan making that a lot easier and years of consoles with 8 small Jaguar x86 cores forcing a balanced design for all game engines as there is no single thread that can do the majority of the work).
If I was stuck with a stock-speed 2xxx CPU, I'd get the GPU upgrade now (1060 is a great choice) but keep an eye on my budget and be thinking that at some point in the next year I'll be looking for new RAM (DDR4), a new CPU, and mobo to drive the two. Transfer the rest of the system over but then have a great base for the next 5 years (like the last CPU has lasted you since 2011) which means you'll be able to put a new GPU in there in maybe 3 years without being CPU-limited.
* Intel paid nVidia $1.5bn as a "licensing fee" to end all patent disputes around x86 and agree to not develop their own x86 CPU in 2011. That deal has been pushing $66m to nVidia every quarter ever since. So that's how much Intel value not having nVidia with a x86 patents. The entire of AMD (x86 patents and all) has a market cap of about $5bn right now. You can see a point where someone wants to spin off the GPU side of the company and sell the rest for the patent portfolio.
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