tete-a-tete vs head-to-head

tete-a-tete is a noun but head-to-head is not a noun.

Word	Noun	Adjective	Verb	Adverb
tete-a-tete	Yes	Yes	No	No
head-to-head	No	Yes	No	Yes

As adjectives, tete-a-tete and head-to-head are synonyms defined as:

tete-a-tete (noun)	head-to-head (noun)
small sofa that seats two people
a private conversation between two people

tete-a-tete (adjective)	head-to-head (adjective)
involving two persons; intimately private	inconclusive as to outcome; close or just even in a race or comparison or competition
	involving two persons; intimately private

tete-a-tete (adverb)	head-to-head (adverb)
	even or close in a race or competition or comparison