How are you determining a "bottleneck"? What resolution? What games? What in-game settings? What refresh rate?
Please post your full system specs.
Ultimately, both chips are 6c/6t parts. The 9600K is a good margin faster in clock-speed, but if you're being "bottlenecked", it's more likely to be from a core count than it is from strictly clock speed.
Also, a 9600K will require an aftermarket cooler and (preferrably) a Z series motherboard. Increasing the cost substantially. For the likely minor gains, it would be a pretty big waste of money.