After a bit of finagling, I wrote an anydice calculation that should produce the probability distribution of the highest absolute ability score from this method. Unfortunately, it doesn't actually run on anydice.com due to a low runtime limit; I don't know if a local equivalent exists that could be allowed to run longer and obtain those results.
If it is possible to run with a lot more efficiency or runtime, this calculation should produce probability graphs for each player's highest and total scores. Similar graphs could be produced for second highest, third highest etc.
While, as I mentioned, I haven't been able to run all those calculations, a few points are immediately obvious. First: Player 1 will always have the highest "primary stat", but the lowest "secondary stat", as well as the largest variance between their highest and lowest stats. That would lead Player 1 to perform best at a class where their primary stat is pretty much all they need. On the other hand, Player 4 would have the lowest primary stat and the highest secondary stat, as well as the lowest variance between highest and lowest stats, performing best in any class with their two best stats very close in importance and/or where their dump stat needs to be a little higher than terrible. Players 2 and 3 would be between them.
Overall I'd say Player 1 gets the best out of it; their first and third highest stats are the best, with their second best on the low end, while Player 4 has the worst first and third stats, and a higher second seems unlikely to make up for that. This might be subjective, but to me there's a very major gap between the values of the highest 3 and lowest 3 ability scores, so Player 4 having the best 4th and 6th highest scores has almost no impact in my opinion.
Finally, in an attempt to get some useful graphs at all, I made a simpler simulation for just the "Highest stat". First I tried checking distributions for a few alternatives. The one that most closely ended up matching the distribution of "top ~17% scores" on the normal rolling system was the one called "skewed high distribution", so I made this calculation intended to estimate what scores each player would get for their highest score. Keeping in mind that I just eyeballed the distribution for that, it shows Player 1 with over 70% chance to have their highest score be 17 or 18, while Player 4 has over 70% chance for their highest score to be only 15. Checking the alternative distributions gives similar results: Player 1 usually has at least 60% chance to get a 17 or 18, while Player 4 has less than 1% chance.
For an alternative measure, I've done some math by hand to generate a "typical" pool, i.e.
probability of generating a score * 24 attempts = expected number of that score, and assigned them in accordance with your procedure to get these results:
- 17, 14, 13, 11, 11, 6
- 16, 14, 13, 11, 10, 7
- 16, 14, 13, 12, 10, 8
- 15, 15, 12, 12, 9, 9
Going at the calculation from this angle, we can see that the advantage Player 1 gets in their Highest stat is significant since there's likely to be only one 17 or 18 score in the entire pool, but differences between players in the second through 4th stats is minimal because 11-14 are very common in 4d6 drop 1. There is an even larger disparity in the lowest stat because of a flatter tail, but a "dump stat" is commonly desirable and I doubt the other players would be unhappy to move points from their lowest to their highest stat.