at any rate vs in any event

at any rate and in any event both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at any rate	No	No	No	Yes
in any event	No	No	No	Yes

As adverbs, at any rate and in any event are synonyms defined as:

at any rate and in any event: used to indicate that a statement explains or supports a previous statement

Other synonyms of at any rate include anyhow, anyway, anyways, in any case.

at any rate (adverb)	in any event (adverb)
used to indicate that a statement explains or supports a previous statement	used to indicate that a statement explains or supports a previous statement
if nothing else (`leastwise' is informal and `leastways' is colloquial)