Another '82 baby over here!
To my mind, "old school" in the purest sense is the first 20 years of the run, not because 20's a cool number but because the time around the 20th year just happened to correspond with some shake-ups, like the deaths of Henson, Raposo and Northern Calloway, and other factors that sort of left the show a bit directionless for a little while until they decided to update their image a little and add the Around the Corner setting. (I think Henson's death had much more of a long-term impact than short. At first it didn't really change anything, but over the years as the material has gotten tamer and less saucy, I have the suspicion that if Henson and his immeidate influence were still around, he wouldn't have acquiesed to the new approach quite as much as has been done.)
But even though the Around the Corner era was a BIT different, it wasn't really a drastic change. The basic character of the show was still the same, and plenty of old material was still floating around, which of course gave it certain consistency of personality through the decades.
Then came 1998, and with it Elmo's World, mass retirement of older stuff, and a rather noticeable change in writing tone. (Besides the new research and the shift to a younger target age, I think the departure of Jon Stone had the most to do with that last part.) And then 2002 and the Really Big Shake-Up.
So even though the '90s to me are kind of a gray area when it comes to "old school" in the sense you guys mean, to me anything before 1998 is what I call "the old show." "The new show" is the amorphous and continuously changing creature that's been airing since.
1969 - 1997 = Sesame Street 1.0
((1998 - 2001 = Sesame Street 1.5
))
2002 - present = Sesame Street 2.0