Hi. I am one of the authors the D&D Hârn Guide. I play HârnMaster and D&D/D20 so perhaps I can shed some light here.
For a good description of HârnMaster (Core) go here:
http://www.lythia.com/articles/hmintro.php
There is a very good comparison between D20 and HM here:
http://www.warflail.com/downloads/
HM is designed specifically for use with Hârn World. As has been mentioned, Hârn is a very low magic (powerful magic does exist, but it's very rare), historically "accurate" campaign world, modelled after 11th century England. You don't play heroic characters in Hârn. You play normal people - knights, soldeirs, cutpurses, bandits, tribal hunters/warriors, street urchins, merchants, vikings, priests... you can even play escaped slaves, serfs, normal villagers, a baker, the village reeve, etc, if you want. So it's not so much "adventurers" having adventures as much as normal folks from society having adventures. You might think of HM as a game system for the NPC classes you find in the DMG.
I must take exception with the notion that HM is very slow. Personally, I find HM combat faster and smoother than D20 combat, but not because it is simpler (it isn't), but because it is much less tactile. The GM isn't burdened with having to remember the bajillion and one modifiers to all the combat rolls due to feats, magic items, and special abilities (something I lack the ability to do well) that the PCs and monsers have. He also doesn't have to arbitrate variable DC targets - any modifiers are applied to any already established number.
Compared to Rolemaster, HM is zippy stoopid fast.
Granted, I know some people who think HM is WAY slower than D20, but I attribute that to differences in GMing style.
Like D&D, HM is a great system for what it's designed to do. D&D is for high fantasy, high adventure, heroic play where the point is for your character to progress in power by a system of rewards for overcoming obstacles. HM is for gritty and dark, heavy roleplaying, more freeform kind of play where the point is for your character to help progress a story by interacting with NPCs and the environment; developing your character's stats is secondary.
As for combat, if your idea of combat is that getting stabbed, poked, prodded, smashed, skewered, etc, with ANY medieval weapon is going to hurt a lot, and likely cause you to fall to the ground writhing in pain, then you'll like HM.
Hope that helps.
A definite bad thing about HM is that it isn't complete. There are a few rules suppliments that never saw the light of day. But there's TONS of houserules to fill the gaps.
-Shane9
Shadow of Bukrai
http://www.dndharnguide.addr.com
Be sure to visit
http://www.swordsandshields.org which will be
THE place for D20 Hârn.