The number of Grand Slams is the most relevant all-time criterion. Most people do consider other criteria, but only if two players are tied in Slams. Other criteria would be some kind of "tie-breaker" in case two players are tied in Slams. This is specially true if two players played in the same era. If two players played in the same era and one of them won less Slam titles, he is simply worse. It would be completely unobjective to rank a player with less Slams over a player with more Slams when they played in the same era. The player with most Slams playing in the same era is the greatest of his era, as other players playing in the same era were not talented/good enough to win as many Slams as him. Because Djokovic is the member of the Big 3 with less Slams, the ad hoc excuse that you do not need the most Slams to be the greatest is typical from Djokovic fans. But for the rest of mortals outside Djokovic fans, everyone knows that he who wins the most Slams is the greatest of his era.
Respectable but strongly disagree, Muster vs Bruguera is a quite clear exception imho. Same era, the player with less slam is the greater by good margin. I think Becker vs Wilander is still a good example and i put Edberg over Wilander too.
And this is from a Nole fan who thinks that Djokovic, at the moment, is greatless than Rafa(I don't want put Federer in the discussion now, competition topic is too large).
With regard to your peak ELO point, I must say that ELO can never be used as a criterion to rank player's greatness. ELO is originally applied to chess, and it is misused out of context in tennis. Plus, there is no official ELO tennis rating, there is only an official ATP rating. Unoffical ELO tennis ratings tend to differ depening on which webpage creates one (Ultimate Tennis Statistics gives a different ELO rasting to players than Tennis Abstract). It means they are unreliable.
Not checked, but I think difference between rantings are marginals. I used UTS one, btw.
Peak ELO can never be a GOAT criterion. Those who praise ELO do not undertand the phenomenon of ELO inflation. We cannot ignore ELO inflation, the phenomenon by which players from the present always have higher ELO rating than players from the past. Murray has a higher peak ELO than Sampras and it does not mean that his level was superior. It only means that Murray could inflate his ELO with victories against the Big 3, while Sampras could not increase his ELO as much because his victories were against players with lower ELO rating. The same phenomenon occurs in chess, players from the present have higher ELO than in the past due to ELO inflation. Yet, no one
claims that a contemporary player like Aronian is greater than a legend like Fisher only because the former achieved a higher peak ELO with the ELO inflation.
You can have inflaction o deflaction, but not sign of either is presents in UTS rating. Top player ratings in early '80s was high, in late '90 and early '00s was low and they was high in late '00s and early '10s. This has a great correlation with top players win % in those seasons.
Sampras has a low Elo Peak because he was inconsistent outside slams.
Elo is clearly not the most important GOAT criterion, but is a good indicator.
