Out of all the anniversary seasons mentioned above, I think Season 30 is my favorite out of those, mainly because there were a lot of classic clips being shown at the time, often made to seem like they were happening on that very day, which I actually liked.
According to Muppet Wiki, one of the main curriculum goals of that season was to expose many of the classic songs, and it seems many classic songs had gotten new versions, in addition to showing the classic clips. Interestingly, I recall the season two Rubber Duckie was in two episodes that season, while a new version (I think) was introduced that year as well, in addition to one episode showing a film insert that had Ernie singing Rubber Duckie over footage of kids taking baths.
Of course, considering the focus on reintroducing old songs, it seems there are quite a few that weren't shown at all (I watched the show on an almost daily basis that season, and only missed a few episodes). I don't recall that season having classic songs like Doin' the Pigeon, Bein' Green, or Elmo's Song. But it did have a few segments that I barely remembered from childhood but hadn't seen too often, like The Ballad of Casey McPhee and the Teeny Little Super Guy segments.
I hadn't watched much Sesame Street in seasons 27 or 28, then watched a bit more during season 29 (and several season 29 episodes would be reaired quite a bit after season 30 premiered, including all the "Slimey goes to the moon" episodes being rebroadcast in the weeks before season 31 premiered), and it seems like a lot of classic characters were shown significantly less in season 30, while they seemed to appear quite a bit in season 29. It seems Kermit was only in about 7 episodes of season 30, most of them being news segments, and there was very little-to-no Guy Smiley, Sherlock Hemlock, Biff, Sully, or Forgetful Jones starting then (a few years ago I saw on Muppet Wiki that there was at least one instance each of them airing classic Guy Smiley and Sherlock Hemlock segments in season 30) while I think segments with them were common in season 29.
Of course there have been a few times where I've seen people from Sesame Workshop use the addition of Elmo's World as an excuse for the lack of certain characters. For example the official Sesame Workshop page had something answering questions from fans, one about the lack of the Twiddlebugs, saying that Elmo's World bumped out time for them (I assumed they stopped making new Twiddlebugs segments because of the deaths of Jim and Richard and lack of involvement from Frank, though it seems new segments with the Twiddlebugs were becoming scarce in the 1980s. While EW is long, I feel they could have managed to squeeze in time for segments with certain characters. It makes more sense to not see more characters now when most of the show is made up of long segments that have to air on a daily basis).