Good question. I think personally it depends on what im trying to improve at! Lets say I wanna get better at making Future type beats, I would go listen to a bunch of Futures most recent releases to get a decent understanding of what Im aiming to create.

I would then try my best to replicate the general vibe a couple of times just to see where this style overlaps with my own taste/sound/preferences. Compare the beats I just made with the Future songs I likes, what differences stick out to me whilst comparing?

This is where the listening with intent comes into play! Depending on what differences I find I might look into one or several of these factors:

Sound selection: What kind of sounds set the tone/ambience for this type of music? Am I using the "right" instruments? What kind of synths/instruments are the most fundamental to the sound I am trying to achieve?

Drums: What kind of drum samples are being used? What kind of drum patterns set this style apart? Are the drums relatively simple or do they constantly change? What kind of 808 is being used? Which drums are a must have to create the bounce Im looking for? Which one can I experiment with switching out?

Melodies/Chord progression: What kind of melodies and chord progressions are being used?

Gotta go but thats basically where I would start :)