user23713: 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?

user4418: 
He thereby claims that games are easier on Lichess than on Chess.com.

If his claim that the players on Chess.com are better than the players on Lichess is true then his conclusion is trivially true.

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

This makes no sense. The rankings generated by a rating system like the ELO algorithm are relative rankings, by definition, not absolute.
No knowledgeable football (soccer if you are from the US) fan would suggest that the team at the top of the Moldovan national football league was the equal of the top team in the Spanish or Italian leagues yet all three leagues use basically the same ranking system. Why on earth do you think chess is different?

user13433: Lichess recently added a concise explanation to its site:
Chess rating systems
Important points:

Chess.com uses the Glicko-1 algorithm with an initial rating of 1200.
Lichess uses the Glicko-2 algorithm with an initial rating of 1500.
Neither of them uses the Elo algorithm (not ELO - it's not an abbreviation).
Furthermore, it doesn't make sense to compare the ratings even if both sites used the same system, as they have different player pools.

If we are just talking of abstracted playing strength, the assertion that one site is "easier" than another still doesn't make sense. Elo and Glicko systems all have in common that if you get matched with players with the same rating as you have, they will on average have the same strength. So even if one pool is better overall, you as an individual wouldn't notice as you would be matched to comparably skilled players on both sites.
Unless your friend is a Super GM, of course.

23713: <p>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. <em>He thereby claims that games are easier on Lichess than on Chess.com.</em></p>
<p>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 <strong>X</strong> on Chess.com then my strength shall be <strong>X</strong> 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.</p>
<p>Who is right and who is wrong? What arguments would you guys provide to my friend ,or to me for that matter?</p>
 4418: <blockquote>
<p>He thereby claims that games are easier on Lichess than on Chess.com.</p>
</blockquote>
<p>If his claim that the players on Chess.com are better than the players on Lichess is true then his conclusion is trivially true.</p>
<blockquote>
<p>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</p>
</blockquote>
<p>This makes no sense. The rankings generated by a rating system like the ELO algorithm are <em>relative</em> rankings, by definition, not absolute.</p>
<p>No knowledgeable football (soccer if you are from the US) fan would suggest that the team at the top of the Moldovan national football league was the equal of the top team in the Spanish or Italian leagues yet all three leagues use basically the same ranking system. Why on earth do you think chess is different?</p>
 13433: <p>Lichess recently added a concise explanation to its site:</p>
<p><a href="https://lichess.org/page/rating-systems" rel="noreferrer">Chess rating systems</a></p>
<p>Important points:</p>
<ul>
<li><strong>Chess.com</strong> uses the <strong>Glicko-1</strong> algorithm with an initial rating of <strong>1200</strong>.</li>
<li><strong>Lichess</strong> uses the <strong>Glicko-2</strong> algorithm with an initial rating of <strong>1500</strong>.</li>
<li>Neither of them uses the <strong>Elo</strong> algorithm (<em>not</em> ELO - it's not an abbreviation).</li>
<li>Furthermore, it doesn't make sense to compare the ratings even if both sites used the same system, as they have different player pools.</li>
</ul>
<p>If we are just talking of abstracted playing strength, the assertion that one site is &quot;easier&quot; than another still doesn't make sense. Elo and Glicko systems all have in common that if you get matched with players with the same rating as you have, they will on average have the same strength. So even if one pool is better overall, you as an individual wouldn't notice as you would be matched to comparably skilled players on both sites.</p>
<p>Unless your friend is a Super GM, of course.</p>
