I think Oates should probably be in the HHOF, but I also think he's quite over-rated.
Brilliant playmaker, yes, but lots of warts there. Goalscoring record (save for one year) isn't great. Mediocre defensive player - very over-rated in that regard by people who equate faceoff ability with defensive play ... especially in his pre-Washington years he was quite poor. And he was a big-time mercenary who feuded his way out of organizations several times during his career and wasn't considered a great team guy. Never played a single game of international hockey, which is amazing in this era. Never won anything.
But all that said, 1000 assists should put you in the HHOF, full stop.
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As for Oates vs. Turgeon, I don't think there's much difference there at all.
Oates had a better career, but largely because Turgeon had a knack for getting hurt during his best years, and lost 4 top-10 finishes (and a potential Art Ross in 1999-00) to injury. If Turgeon could have stayed healthier, it would be a near dead heat.
And I don't think there was much difference in their intangibles. Oates was a better faceoff man, but otherwise? Meh.
To me, one guy just got unfairly lambasted for his lack of grit/character while the other got a free pass.