My preference is to analyze in ChessBase. Both sites serve well enough for casual analysis, but neither offers quick and easy access to reference games. Neither site offers you storage flexibility to save your analyzed games in a manner of your design.
Do you find it easier to analyze your games on Chess.com or Lichess?
I use droidfish because it is fast on my phone, but it has disappeared on google play for some reason.
The thing I care about most when comparing the two sites is the quality of post game analysis. Personally I find the Chess.com interface much easier to use and learn from. Recently I had some friends tell me the opposite. It's my understanding that the strength of the engines is the same between the 2 sites. Do you have a preference and if so why? I'm asking in regards to this feature only.
I prefer lichess analysis for the same reason I prefer lichess in general... it's less cluttered with loads of crap, and it takes fewer clicks to get what you want.

Chess.com !! But, if you really want some very good depth and analyze like a pro, then I would say that chessbase is the best one. Almost every titled player uses this software for analysis and preparation.

If you want a rating on your moves then chess.com but if you only want to know the best move then use lichess

This site rigs games so when you lose, you lose based on some tactical thing they are marketing. It's not hard to program an AI bot to calculate lines out that will steer the game to a position. You can do that easily as human by just playing a line solidly and consistently.
Can you elaborate on this? I'm not sure I follow you.
The thing I care about most when comparing the two sites is the quality of post game analysis. Personally I find the Chess.com interface much easier to use and learn from. Recently I had some friends tell me the opposite. It's my understanding that the strength of the engines is the same between the 2 sites. Do you have a preference and if so why? I'm asking in regards to this feature only.