Bayān al-ḥāl tells the listener what the state is like. The sun-and-stars image reveals how one prominent ruler overshadows others.
Bayān miqdār al-ḥāl measures a quality already recognized. The raven's feather specifies the intensity of blackness.
For example:
“Zayd is brave like a lion” can state degree when the listener already knows he is brave but wants to know how brave.
“He is like a lion in battle” can reveal his combative state when the listener does not know what he is like there.
The purpose is determined by context, not by the mere use of “lion.”