There are a few issues.
As noted, there are several other games, including old school D&D and clones, Runequest, and WHFRP that may be closer to what you want. There are also other D20 games like Conan and the excellent Grim Tales.
On the other hand, I have done lots of 3E and 4E with certain elements of "old school style", and on that basis:
If the issue is just dungeon delving, you can certainly do that in 3E or 4E. If it is delving with traditional D&D isms, again you can do that in 3E or 4E.
If you want resource management, 3E and 4E have that. You can even track rations, amo, components, etc, if you want, though many groups probably don't.
If you want to terrorize the players, again you can do that. In 3E, its pretty easy, but swingy. In 4E, its a little harder, and time consuming, if you are talking about a fight. 4E is a bad edition to just kill charecters for the sake of doing so, but 4E remains the best edition in terms of calibrating how tough you want a fight to be.
If you want environmental challenges, again, 3E or 4E have it. I like that in 4E, things like exposure can lead to loss of surges. And in some cases there may be fewer spells/rituals to ameliorate these challenges. On the other hand, 4E may also involve some kind of skill challenge. On this I am more indifferent.
You can certainly do traps or puzzles in 3E or 4E. There are conversions of Tomb of Horrors for each...and 4E also has a sequel to it (with the same name). These are also good examples of giving alternatives to combat encounters in the dungeon and really bringing exploration to the fore.
This also points out one deep flaw with early 4E: its attempt at making everything about combat, including traps. Traps in combats are fine, but only combats get awfully boring and are ironically uncinematic (you would be surprised at how little time is spent fighting in action films). Its called pacing, and default 4E could be pretty terrible at it, though latter adventures do a much better job.
Any ways, to get to a point: what is your goal? If it is to keep some elements of 3E or 4E but to put more emphasis on exploration and dungeon and wilderness non-combat tactics and danger, you can certainly do that. If that is your goal.