Look at it this way.
The higher the refresh rate of the monitor, the smoother the experience.
If you have a 60Hz monitor, then your frame target would be 60 FPS. Same for 120 and 144Hz monitors.
You'll need a high end graphics card if you're going for 120 or 144Hz monitors, since 144 FPS is much harder to achieve than 60 FPS.
If you can achieve that framerate, however, then you'll get a whole different experience from the 144Hz monitor.
One word of advice, however.
Don't go for a monitor that has very high refresh rate, because today's games use a lot of CPU horsepower. So most probably you won't be able to achieve the 120 or 144 FPS target, in which case you'll get screen tearing.
Of course, the final decision is yours.