So I usually play on Lichess now a days while my friend plays on Chess.com. He keeps telling me that Chess.com is harder and has more players and more serious players, therefore the games are harder and players are better than on Lichess. He thereby claims that games are easier on Lichess than on Chess.com.

For me this claim makes no sense because both sites use the same ELO algorithm, which is a mathematical object, independent of which players play on which site. If my strength is X on Chess.com then my strength shall be X on Lichess, as well. The rating number could be different since that can be manually magnified, but the strength of a player cannot be magnified obviously.

Who is right and who is wrong? What arguments would you guys provide to my friend ?

So I usually play on Lichess now a days while my friend plays on Chess.com. He keeps telling me that Chess.com is harder and has more players and more serious players, therefore the games are harder and players are better than on Lichess. He thereby claims that games are easier on Lichess than on Chess.com.

For me this claim makes no sense because both sites use the same ELO algorithm, which is a mathematical object, independent of which players play on which site. If my strength is X on Chess.com then my strength shall be X on Lichess, as well. The rating number could be different since that can be manually magnified, but the strength of a player cannot be magnified obviously.

Who is right and who is wrong? What arguments would you guys provide to my friend ,or to me for that matter?