I played D2 HC; leveling or PvE in D2 was not much harder than softcore. When I had a duel with a wanted sorc (illigit killer), however, my adrenalin went up sooo high (I died there in the end), which I could never forget and to which there's almost nothing comparable even in real life.
Simply put, hardcore "make[s] my seated heart knock at my ribs" (to quote from Macbeth).
I play HC cos it's more of an intense game experience. I love to play relaxed and chilled-out. So in HC there is NO HURRY whatsoever. You level in the same spot for more time than in SC and you advance more carefully, thus slower.
The group you play in is more important. Teamplay is on top of the list, even though you might play with randoms. And at a certain level, you will not find bloody amateurs in HC anymore, so people know what they are doing, thats even more fun.
The bad side is the death. Of course it sucks when you die at a certain level. So the motivation for me is NOT TO DIE, therefore play slow, play concentrated, never rush and enjoy every single minute you're playing.
Compared to SC (what I dont like in SC that much), you can wipe your way through the enemy. If you can't kill a boss pack, then you die 10times and in the end the enemy will be dead. In HC you need strategy, team, equip!, and skill of course. This is what makes it interesting for me.
I'm just a casual player, therefore I love HC, cos u go slow and easy. In SC you just farm your way through until u get sick of it. There is no challange.
So everybody plays the way the like. If you don't see a personal reason to play HC, then enjoy the SC version. :-)