I think the "2nd edition feel" really began with the D&D Known World Gazetteer series, even though that series began during 1st edition days and was for a different ruleset from either 1e or 2e.
But the hallmarks of the series: intense setting detail, books that are fun to read, story hooks and metaplots tying the setting together, and increased character customization all became defining characteristics of the 2e era.
You can see it in some of the 1e Forgotten Realms stuff, too, which read like 2nd edition books even though they use 1e rules.
Now, 3e has the character customization angle covered in spades. Prestige classes, feats, new core classes, substitution levels, and everything else do everything kits did and they do them far, far, far, far, far, far, far better. Kits were stupidly made, unbalanced, and arbitrary. Most 2e kits can be represented better in 3e using no rules beyond the PH, and those few for which this isn't the case were always more like new core classes anyway.
In some ways, Eberron feels like a 2nd edition setting. So does the 3e Forgotten Realms. The only real difference is that their supplements sometimes get drowned in prestige classes, feats and the like. This isn't really antithetical to the 2nd edition approach, given all the class books and Player's Option books we were plagued with at the time, but once upon a time the campaign setting books had a slightly better ratio.
There were lots of bad things about 2e that I don't feel even a little nostalgic for. First and foremost was the graphic design in early 2e, where the section headings had bright blue font, clip art from old Dragon Magazines and the like, ugly black and white drawings, gigantic illustrations above every page which were identical for every page in the chapter, and every chapter or so there's be a big full-color painting cribbed from the cover of an older adventure or Dragon issue. Late-'80s 1e and the Known World Gazetteer stuff had just begun to make Dungeons & Dragons look attractive and suddenly they had to push everything into an incredibly ugly, uniform style. I guess they thought making all their products look the same made them more "professional" somehow? I know Jim Ward must be to blame, as the Fast Forward stuff has a very similar hideousness without the benefit of free access to old Dragon Magazine art (and, in that respect, the Fast Forward stuff had a very "second edition feel").
Later 2e had higher production values and a tendency to let a single artist define a setting. Dark Sun had Brom, Birthright had Tony Szczudlo, and Planescape had Tony DiTerlizzi - all cases where the artist was co-creator of the setting. The resulting uniformity in design was beautiful. Of course, they had done that before with Dragonlance and Larry Elmore, but it had been a while since they had thought of it.
As the settings' defining artists moved on to other projects, the various settings lost this (although Baxa was a pretty good substitute for Brom). And Wizards of the Coast, for whatever reason, didn't seem to care as much about making the books look good (which is weird, but I guess they were putting all their graphic design resources into Magic: the Gathering and could only get crack-smoking monkeys to do their 2nd edition AD&D stuff). Getting Todd Lockwood and Sam Wood to create a uniform 3rd edition look was a good move, but then they squandered that by letting several dozen wildly divergent artists interpret every single 3e book. If they could just say something like "Lockwood, you do the PH; Sam, you do the MM; Reynolds, you do the MotP" they might've had something.
The best graphic look in 3e has been in Forgotten Realms and Eberron. If one of the hallmarks of the "2nd edition feel" in the positive sense of the phrase is consistent, beautiful graphic design, those settings have it (at least, occasionally they do).
I'm not sure I've said anything cogent - I think I've been rambling - but I'm done now.
