peerlessness vs excellence

peerlessness and excellence both are nouns.

Word	Noun	Adjective	Verb	Adverb
peerlessness	Yes	No	No	No
excellence	Yes	No	No	No

As nouns, excellence is a hypernym of peerlessness; that is, excellence is a word with a broader meaning than peerlessness:

peerlessness: The state or condition of being matchless, of having no equal.
excellence: the quality of excelling; possessing good qualities in high degree

peerlessness (noun)	excellence (noun)
The state or condition of being matchless, of having no equal.	the quality of excelling; possessing good qualities in high degree
	an outstanding feature; something in which something or someone excels