by choice vs deliberately

by choice and deliberately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by choice	No	No	No	Yes
deliberately	No	No	No	Yes

As adverbs, by choice and deliberately are synonyms defined as:

Other synonyms of by choice include advisedly, by design, designedly, intentionally, on purpose, purposely.

by choice (adverb)	deliberately (adverb)
with intention; in an intentional manner	with intention; in an intentional manner
	in a deliberate unhurried manner