Don't know if it'll still work but it did a year ago and it's a starting point.
For serious play i'd say it is chess.com, playchess.com(Chessbase parent), ICC and only then Lichess.
In some UI aspects Lichess does feel nicer and lighter.
That's just the nature of the open-source model, the money is sorely lacking for promoting chess professionally.
Maybe some day the Patreon model will transfer to attracting top GMs to Lichess but for now they might check out Lichess and then leave immediately such as was the case with Wesley So earlier this year.
By comparison chess.com has the money to attract strong titled players to its online tournaments and even sponsor strong over the board tournaments such as the recent Isle of Man super Swiss.
serious: ICC, for the competition. casual: lichess, for the dramatically superior UI and value than any other site edit: the personal analytics alone make lichess superior to chess.com and other long time inferior sites like chesscube.
playchess and chess.com are relics, though chess.com survives on promos and articles and such.
You might be right that ICC is more serious but chess.com has been making great strides in providing nifty web and online apps.
chess.com sponsors online and regular OTB tourneys like the recent Isle of Man super Swiss, not sure what ICC does.
I feel that ICC is the one that is a relic from 1990s.
In all fairness I had not played on ICC in 10 years ever since they tried to blackmail me in ordering a membership lest my 10 years of tens of thousands of stored games on them would vanish. (I started on ICC when Sleator split/took the code from original ICS in mid 1990s).
I just checked ICC online presence and played a few games as a guest, there was 1 GM and one IM online.
Even lichess has more titled players than that.
My bias is that chess.com offered me a full membership as a lowly FM while ICC didn't offer anything but blackmail.
Again, I could be wrong, but the impression to me is that ICC is still sleeping on its laurels from late 1990s.
Another note is that all the other chess sites (lichess, chess.com, playchess) have a notably more international feel.
Mostly because Lichess is written in Scala[1], but the engine probably helps a bit too ;-)
Love the tagline, "lichess.org: the forever free, adless and open source chess server"