insight vs sixth sense

insight and sixth sense both are nouns.

Word	Noun	Adjective	Verb	Adverb
insight	Yes	No	No	No
sixth sense	Yes	No	No	No

As nouns, insight and sixth sense are synonyms defined as:

insight and sixth sense: grasping the inner nature of things intuitively

insight (noun)	sixth sense (noun)
grasping the inner nature of things intuitively	grasping the inner nature of things intuitively
the clear (and often sudden) understanding of a complex situation
clear or deep perception of a situation
a feeling of understanding