head-to-head vs tete-a-tete

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

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

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

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

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

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