There are many similar features. Overall the UI on ChessMonitor is much more focused on statistics.
Another key feature Lichess does not have, is the Openings page. It is very powerful when used correctly. You can look at your openings and immediately see for which openings you might need to consume more theory (or which you should not play at all).
The main killer feature I see is combining multiple accounts. Are there any other features didn't notice?