It's hard to remove our knowledge of Edmonton's being a dynasty, and Pittsburgh not. It just swings it in Edmonton's favor.
But trying to just isolate those three years in the OP's topic, we have regular season finishes like this:
Edmonton
1986 - 1st overall (.744)
1987 - 1st overall (.663)
1988 - 3rd overall (.619)
AVG.: 1st overall (.675)
Pittsburgh
1991 - 7th overall (.550)
1992 - 6th overall (.544)
1993 - 1st overall (.708)
AVG.: 5th overall (.601)
Then, we have combined playoff records like this:
Edmonton
38-11 (.776)
Pittsburgh
32-13 (.711)
I think the main reason the Oilers slipped to 3rd in 1987-88 is (a) Canada Cup hangover; (b) adjusting to life without Coffey (and Moog); and (c) disinterest in regular season in general. In any case, I guess both RS and playoffs' records have to be in Edmonton's favor, although I think Pittsburgh probably had a bit harder competition in round one at least. (Both teams could wipe the floor with hard competition anyway: The '88 Oilers went 8-0 against the 1st overall and the 5th overall team, while Pittsburgh went 8-0 in the '92 Conference series and Cup Final.)
Offensively, maybe we'll call them even. Both have the nuclear weapon at center that will produce big points regardless of anything. I think the Pens had a more fearsome power-play, partly for reasons I'll get into below... But, is Lemieux going to be healthy and in the line-up (always an issue), and is Jagr really "Jagr" yet? He's sort-of arriving in the '92 playoffs and the 1992-93 season, but in both 1990-91 and 1991-92 he's not quite a stud yet.
Defensively is where it gets interesting. Coffey was awesome in the 1985-86 regular season (Norris; more goals scored than Orr; +61), but he was poor in the '86 playoffs. Then, he was oft-injured and less effective in the 1986-87 season and playoffs (and did they really need him in '87? They scored 13 goals in a playoff game when he was out with injury). It may be a controversial opinion, but after '86 I feel Edmonton was better with Simpson and without Coffey. Beyond Coffey, the Oilers had only Ruotsalainen as an offensive D-man and then only for the '87 run. Besides those two, it's stay-at-home defencemen, although Huddy and Smith could supply a bit of offense. In general, I think Pittsburgh had the better power-play, and it's because they always had two good offensive D-men at the point. Everyone knows I'm a fan of Murphy, and he added a lot and allowed them to lose Coffey in '92. (On the other hand, the Oilers' post-Coffey PP in 1988 was lights-out, so you never know...)
In goal, definitely Edmonton. Fuhr over Barrasso any day, and then you've got either Moog as back-up (another NHL starter until about 2000) or Ranford ('90 Conn Smythe and '91 Canada Cup MVP), so even if the top-guy goes down, you're still totally safe. But do you wanna put Frank Pietrangelo or Ken Wregget in to face top playoff teams?
Then, how did each lose? Edmonton can be forgiven more readily, for sure. Calgary in '86 was a team on the rise, stuffed with top players and some future Hall of Famers, and went on to the Finals that very spring (and then dominated the League, in the RS, from '87 to '94). The Islanders in '93 had their legendary coach and a nice mix of players, but their top guy wasn't even in the line-up and Glenn Healy was in net.
I think the difference, for me, is that the Oil had Messier hitting his prime, whereas Jagr wasn't really peak-Jagr yet in those years (and, truth be told, Jagr isn't generally thought of as a playoff legend; it's sort of the one thing a bit underwhelming on his resume). Not to mention Gretzky, Anderson, and Kurri are all legendary big-game players who always came through in the clutch.