feline vs big cat

feline and big cat both are nouns.

Word	Noun	Adjective	Verb	Adverb
feline	Yes	Yes	No	No
big cat	Yes	No	No	No

As nouns, big cat is a hyponym of feline; that is, big cat is a word with a more specific, narrower meaning than feline:

feline: any of various lithe-bodied roundheaded fissiped mammals, many with retractile claws
big cat: any of several large cats typically able to roar and living in the wild

Other hyponyms of feline include cat, true cat, cat.

feline (noun)	big cat (noun)
any of various lithe-bodied roundheaded fissiped mammals, many with retractile claws	any of several large cats typically able to roar and living in the wild

feline (adjective)	big cat (adjective)
of or relating to cats