Monitors with higher refresh rates have lower input lag and reduced blur when there are fast moving objects on-screen, but if you aren't hitting the advertised refresh rates in games, there is little benefit. If you're playing at 120FPS on a 240Hz display, you aren't any worse off from a 120Hz display. However, you may see benefits outside of games, like navigating your desktop, reading webpages, or scrolling through browser tabs. The more responsive and fluid feel of a higher refresh rate display may be more appealing to you in those cases.