Set the color profile of my external monitor

I have bought an external monitor (ASUSP277) but I have noticed a difference in colours between the monitor and my Macbook Pro.

It's quite annoying, especially since I'm using it for web development. I'd like to have the same colour profile between my Macbook and my monitor, is this something feasible? I've tried to modify it in the system preferences and change the colour profile of the ASUS monitor but there is no profile that comes even close to the one on my MBP.

I'd be more than happy to have your expertise on this one,

Solution 1:

How do you know which one is correct?

The answer is, you don't.
You can't unless you have an external reference.

The only way to ensure colour accuracy is to use a hardware colorimeter.
Entry level start at maybe 50 $£€ though a good one will be closer to 200, or more.
If you are making imagery that others will see, then knowing it was right when it left your machine is vital.