I'm going to answer your question two ways, because either way is going to be a great upgrade for you. There are benefits of shifting over to 4K, but there are also benefits of 120Hz monitors, too.
Going 4K: I have a 4K TV sitting to my left, which goes mostly unused due to its mammoth size. At 39 inches, it's a little too big for a PC monitor, but there are some very nice looking 28-inch 4K-capable monitors coming out very shortly, for under $1000.
These monitors will do 3840x2160 @ 60Hz, which is perfect for gaming and general desktop use. The only issue is having the GPU horsepower to drive all of those on-screen pixels. Do you have enough GPU grunt to do so? Do you enjoy high resolution versus high fRAMe rate (120FPS minimum)? If the answer is 'yes', then you should grab one of the upcoming Dell 4K monitors.
The 120Hz route: On another desk here in my office, I have a 27-inch 120Hz-capable Full HD monitor. I love that it is capable of 120Hz, and if you're playing first-person shooters like Battlefield, Call of Duty or Counter-Strike, then a 120Hz monitor might be a better idea.
But the performance requirement comes into it again. Sure, you don't need to drive the massive amount of pixels that 4K requires, but you need to be doing 1920x1080 at 120FPS minimum in order to get the best out of a 120Hz monitor.
Sideline discussion: The 4K monitor will give you a better picture, colors, and sharpness. The 120Hz monitor will give you fluidity and smoothness. There's a tradeoff for each monitor, so you have to decide which is better in your camp - the higher resolution, or higher refresh rate. Both monitors are going to impress you.