Looking back at 1e (I skipped 2e - yuck), here is what I find missing:
1. The voice of Gary Gygax. This really permeated the books and gave it all a certain mood and feel that I enjoyed. The books were almost like crusty old arcana from another age themselves, which helped to take you into a different mindset. The more modern voice of 3e does not invoke the same mental state for me.
2. The more classical look and feel. Much of the new artwork (with notable exceptions such as swekel and sardinha) has more modern influence - tattoos, black leather, spikes, punk hairstyles, emaciated monsters. Traditional castles and knights in shining armor are gone. I know that many don't agree with my preference, but for me personally this heavily detracts from my ability to "click" with the game. I also think that the heavily saturated color palettes don't help either. They lend a comic book vibe. I prefer a more subtle color palette.
3. More adherence to classical tropes in the races and monsters. Halfings were hobbits with a different name. Gnomes were little forest guys. Now halflings are some strange kind of unique D&D thing and gnomes are Krynnish rennaisance inventors. The illustrations also reflect this shift in direction.
4. Planescape was a seismological shift in the D&D cosmology with implications that were reworked as more integral/core in 3e. What was once something really odd and suggestive of Dante, Ptolomy, the Golden Bough, the Eddas, and other mythological sources became something more like an urban cosmopolitanism that suggests Star Wars more than anything else. I know that lots of people like Planescape, and while I think it's pretty nifty on it's own I really don't like feedback effect it's had on standard D&D.
5. More freeform advancement/rewards. Things were more ad-hoc regarding what you threw at players and how quickly they advanced. In 3e, the baseline, while it may be deviated from, strongly encourages a very linear, predictable, and fixed progression. It even goes so far as to regulate the amount of magic items you have, and makes characters feel less competent if they deviate from the baseline. Of course rule 0 is there, but nonetheless players come to expect this because it's in the rules.
6. A more abstract system of combat and power representation. In 1e, combat was abstract and open to wide descriptive liberties. 3e shortens the combat round to represent every swing of the sword and also introduces a little bit of power-up/special street fighter move combo effect created primarily by the advent of the feat system. While the feat system has it's advantages, in my opinion these very specific moves increase video game feel at the expense of literary feel.
7. Strong character archetypes. The simple choices of 1e presented simple and bold archetypes. I feel this is weakened in 3e most notably by the proliferation of prestige classes. With 100 archetypes, each one individually starts to feel less archetypal.
8. Diaglo's blood rituals and cultists is also on the money for me. You have to go to d20 publishers for the good stuff.
Some of this is just cosmetic stuff, but I don't discount the value of an evocative atmosphere. I do think it has an ephemeral effect on play - certain preconceptions that everyone brings to the table. Overall I get more of an old fantasy/literary vibe with 1e - Leiber, Howard, Tolkein, Mallory, El Cid - and that's really where my heart is. I don't deny that much of it is nostalgia, and I also know that far more people prefer the new style than not.
