Discuss and learn French: French vocabulary, French grammar, French culture etc.
yes both are used.
And the two translations "all things considered" and "in the final analysis" could be right.
The more used is "en fin de compte" : it's very used to close a conversation or a subject in a conversation. it's exactly used as "finalement".
"au bout du compte" is more formal, less used in a conversation. More used to introduce an assessment after some actions.