Ciao Alessandro :) it all depends on the attack and release setting on the compressor. So it could be: the transient, the body of the signal and the tail of the sound. Then obviously if the signal after the compressor is lower or higher, if the stereo image is slightly narrower. These are some questions you might ask yourself to think about. Have a good continuation :)

For Dr Compressor, focus on the snare. The more compressed audio will have the snare sounding a little duller/flatter. Careful not to fall for the volume trick. Just because an option is a little quieter doesn't necessarily mean it's the more compressed one. For Compressionist, listen for the different tonal characteristics of the kick and snare as you change attack settings. The higher the ratio, the more squashed the audio will sound however if the attack time is slow (75-100ms) then it will create a loud punch sound. Hope this helps

Hi, Alessandro, one thing I've started doing to help me on compression is how I approach the Compressionist training. Rather than only trying to match the settings to the compressed sound, I also critically listen to the differences among the settings as a separate part of the exercise - how they affect the transient, the coloration of the sound, the position of various parts of the kit in the depth dimension, how they affect the perceived amount of compression, etc. This has helped me get better at picking out subtle differences in compression and how to create those differences, which helps in both of the compression games. Hope this is of use to you.

Thanks for this guys, I have been struggling with this one for a while too. Following your advice I achieved my highest score yet. Wish I'd been been smart enough to ask for help, lol.

For Dr Compressor, I find it helpful to think of compression for what it is… a way to reduce the dynamic range. So it can help to listen to the volume of the elements relative to one another, and then compare how that changes. If the quiet stuff is getting louder relative to everything else, it’s compressed.

Thanks to you all guys, every suggestion has been useful !

I'm not sure that this is the thing, but when I was having problems with compression detection, I found out later that I was mixing up the loudness with compression. Keep in mind that if the sound is louder than the other one, it doesn't mean that it's compressed less. Try to keep in mind that those things are different and pay attention to the release stage of the compressed sound. When it's more compressed, it feels more like an echo on the end, because of the dB ratio.

Also, try to work with real compressors in your DAW. When you see visually hoe the knee cuts down the high frequencies, you can start to understand the conception of the compression better

the attack gets rounded, the length of sustain.
the color of tone. the reverb effect. the pumping. the
leveling of transients.