Just wanted to add my 2 cents.
A lot of good discussion here on low-magic/high-magic, and I just wanted to add a few points coming from someone who went from traditional D&D to a low-magic modern setting, and what we got out of the experience.
1) Like said before, the characters instantly become more about what they are, more than what they have. Even in a game where you can have highly destructive firearms/technology, this still holds true. The group is no longer focused on looting and selling everything they come across, and being really good at something is a lot harder than spending a few thousand coins on the latest do-dad magical thingy. The few odd magical items you come across are much cooler and niftier by comparison, and the focus is on the story not the treasure.
2) Magic became, once again, well, 'magic'. Mysterious. Powerful. Not to be easily trifled with. We used a magic system that you learn about *as you go along* instead of being able to read the entire thing from the book. Magic costs the player to cast, sometimes just a few hit points, sometimes more, sometimes temporary ability damage or other strange stuff, but with no spell slots/spells per day. Find spells as you go, learn them, and try to find ways to cast them more often without killing yourself

. We have no idea what the big bad guy, spirit, demon, etc is totally capable of, though through some research and knowledge may gain some hints or solid ideas about it. Now, when a magical effect happens, people are actually awed by it. If a guy waves his hands and a tree falls down, you can be sure that someone will go "Holy CRAP! What was THAT?!?"
There is still powerful magic, but it is neither easy, nor commonplace. When it happens, you know it, it frightens/excites you in one way or another, and it's something you talk about for a long time afterwards.
3) Most importantly, it has a more tense, invested feel. Call it 'grittier' or whatever you like, but the end effect is that players tend to make better choices with their characters like taking cover, running away from the big nasty six-armed grapple-beast, etc. But people often still do incredibly heroic (read: "stupid") things like jump through windows into the middle of a crowd of heavily armed and hostile men or fend off the hulking demon trying to throw them off of the edge of a 29 storey building with nothing but a bible and their faith, just to save their buddy... and when they survive it, it means that much more in the end. No ressurection and raise dead makes us invest a bit more in our character, because, well, nobody wants to die. And when a character does, it often *means* something, other than loading them up to take to the nearest cleric so they can be fresh as daisies the next day. It makes the choice whether to do something that has a good chance of getting you killed feel a bit more like a choice, and less of a inconvenience. We have actually had characters get whacked *less* with this style of play.
I'm in no way saying it's better; I loved our D&D campaign in all of it's magic-packed and I've-filled-every-item-slot glory, but this way has satisfied our roleplaying needs much, much deeper, so it works for us. When we get back to a D&D campaign, we have plans for balancing the fantastic/fantasy aspect with more of this feel, and I'm very much looking forward to it.