large vs big

large is a noun but big is not a noun.

Word	Noun	Adjective	Verb	Adverb
large	Yes	Yes	No	Yes
big	No	Yes	No	Yes

As adjectives, large and big are synonyms defined as:

large and big: above average in size or number or quantity or magnitude or extent

As adjectives, large and big are synonyms defined as:

Other synonyms of large include prominent.

As adjectives, large and big are synonyms defined as:

Other synonyms of large include magnanimous.

As adjectives, large and big are synonyms defined as:

Other synonyms of large include enceinte, expectant, gravid, great, heavy, with child.

As adverbs, large and big are synonyms defined as:

Other synonyms of large include boastfully, vauntingly.

large (noun)	big (noun)
a garment size for a large person

large (adjective)	big (adjective)
above average in size or number or quantity or magnitude or extent	above average in size or number or quantity or magnitude or extent
having broad power and range and scope	conspicuous in position or importance
conspicuous in position or importance	given or giving freely
generous and understanding and tolerant	generous and understanding and tolerant
in an advanced stage of pregnancy	marked by intense physical force
ostentatiously lofty in style	significant
fairly large or important in effect; influential	prodigious
	serious or severe
	loud and firm
	(of animals) fully developed
	in an advanced stage of pregnancy
	feeling self-importance
	exhibiting self-importance

large (adverb)	big (adverb)
with the wind abaft the beam	in a boastful manner
at a distance, wide of something (as of a mark)	in a major way
in a boastful manner	on a grand scale
	extremely well