Having read newer materials and now reading older materials: I don't really see it. I hear everybody mention it but the writing is about the same (MORE annoying in some places even)
I think what most fans of old editions miss is:
1. Shadowtalk. This was a section present in all FASA supplements where known people in the setting talked about gossip, conspiray theories or simply teased each other on chat rooms, relating to that suplement stuff. It oozed flavor and made the readers get aquainted and even cheering for some setting personas. It was lost in 4th edition.
2. Iconic adventures that set the tone for what was to come: Mercurial, Universal Brotherhood, Harlequin, Bug City, Super Tuesday, Renraku Arcology Shutdown. Even the videogames drank from them (Deadman Switch is a retelling of sorts of Queen Euphoria and UB).
3. Aesthetics. Earlier editions were more dirty and grim (probably due to Bradstreet) while also edgy and funny in a way (probably due to Laubenstein), and the focus on Seattle and the West meant an exotic mix of amerindianism (salish, aztlan) + urban collapse (barrens) + hi-tech (corps) that the artists really brought to life (just look at the cover and logo in first page). Later editions lost this "soul" when they went for a more global/international appeal.
4. Distinct Magical traditions: as an extension of the lose of focus on the American West, the lost of specific systems for each magi tradition (hermetic, shamanic, posession, blood) was seen as another step into a more flavorless state.
Overall, early Shadowrun had a very peculiar vision that was well realized by the writers and artists of the time, and which started to dilute through 3e and was lost by 4e. 5e tried to capture it again with mixed results (I liked some of it) but the spark wasn't there anymore. I think we can blame this on the times. Any product of the 80s would drink from the slightly sarcastic, and absurd, grimdarkness of the time, and Shadowrun wasn't different (see SLA Industries, CP2020 and Vampire 1e, or even Robocop, Terminator and Escape from New York). But of course all this is subjective. The most it can do is help a modern fan to understand the appeal of earlier editions in the eyes of an old fan. It's all a matter of opinion in the end.