Like other answers, let's assume FIDE rating is the baseline for comparison. This is reasonable as it's widely understood by chess players; for example it's what titles like FM, IM, and GM are based on.
Then it is very much possible to compare a player's strength across multiple sites and see which matches the baseline the closest. This comes with some assumptions, like assumptions that online chess performance matches OTB performance and performance across time controls, which appear decently reasonable.
A fairly recent new site lets you compare directly with a graph: https://www.chessratingcomparison.com/Graphs
According to https://chessgoals.com/rating-comparison/, which is based on the player data from their database, chess.com does a fairly accurate mapping:
The Chess.com ratings map pretty closely to USCF and FIDE ratings overall. You can use it generally as a quick mapping to your USCF rating. USCF ratings start at 100, and the Chess.com equivalent is slightly under 500. Between 100 and 1750, the 400-point gap shrinks as the ratings go higher. Above 1750 we see Chess.com ratings are higher than OTB on average. FIDE ratings follow a similar distribution to the USCF ratings. Fewer OTB during the pandemic has not impacted Chess.com to over-the-board comparisons.
Typical bullet ratings on Chess.com are slightly lower than blitz ratings. Rapid ratings start higher than blitz ratings, with a breakeven point around 1900 when blitz ratings begin to be higher. This table also accounts for the change that Chess.com made to move 10+0 games to the rapid category. Chess.com to chess.com ratings have about 7000 data points, USCF 1500 data points, and FIDE 1900 data points. See the complete data below.
Update as of Dec 2021: The page also confirms common knowledge that Lichess ratings have gotten very inflated at lower ratings, and the discrepancy gets smaller for higher ratings, since Lichess's rating system starts users off at a very high starting rating of 1500.
We have also analyzed how lichess.org ratings map to OTB ratings. We combined the first two tables to create the lichess vs. OTB comparison. Lichess.org ratings are generally higher than OTB ratings, and the separation increased in 2021. If you have a lichess rapid rating of 1800, don’t expect to score an 1800 performance at your first FIDE event. Your rating will map to roughly 1420 FIDE or 1270 USCF. The complete data set is below, which maps all lichess ratings to their OTB averages across our survey results.
In particular, a Lichess rapid rating of 1800 corresponds to only FIDE 1420 rating, Lichess rapid 2000 is about FIDE 1660, and Lichess rapid 2400 is about FIDE 2300.
The details of their calculations are here https://chessgoals.com/rating-comparison-explained/
To compare Lichess and chess.com, my rule of thumb is Lichess is roughly 300 points higher than chess.com, give or take 100 points. The hand-wavy explanation is that chess.com starts unrated players at 1200 and Lichess starts at 1500.