profoundly vs intensely

profoundly and intensely both are adverbs.

Word	Noun	Adjective	Verb	Adverb
profoundly	No	No	No	Yes
intensely	No	No	No	Yes

As adverbs, profoundly and intensely are synonyms defined as:

profoundly and intensely: to a great depth psychologically or emotionally

Other synonyms of profoundly include deeply.

profoundly (adverb)	intensely (adverb)
to a great depth psychologically or emotionally	to a high degree; extremely; in high concentration or density
	to a great depth psychologically or emotionally