I have the MG248Q, I think its the newer version of the monitor OP is talking about and I love it.
OP If you don't notice the difference just using the desktop then something is not setup correctly... also in games if your have V-Sync on it will usually limit your frame rate down to 60FPS meaning you will NOT see any major diff apart from the response time so check everything out and let us know.
Now going from 144 ---> 240hz that's a debate on what is "worth" it or not, If your gaming especially esports titles CSGO, PUBG, LEAUGE etc seeing 144 frames per second apposed to 60 gives you a huge advantage at higher levels I cant even play games without a high refresh rate monitor anymore. I also have an RX 580 so I can take advantage of the freesync features of the monitor.
Good Luck!