How exactly increased elo makes lichess worse? I would only argue that because of the number of players chess.com it seems more stable. I really feel every 50 of elo difference.
You're right about the versions, they also have wildly different starting values and very different player pools (I'd argue that more beginners play on chess.com), so you'd expect a substantial elo difference between websites
https://lichess.org/faq#ratings