Short and Sweet-

Softcore-

I've got my uber gear on in the keeps, backed up against a wall. Vortex/Arcane/Waller/Frozen, pinning me down and fighting hard. Ah, screw it if I die I just pay a little bit of a repair bill.

Hardcore- (Real life example)

My Witch Doctor buddy and I are running craters - We are on MP 3 and encounter those big fat meatheads - The yellow champ and his minions. We start the fight and I maneuver past them to avoid a frozen ball. I pull another elite pack of those spear throwers (can't think of their name). I am in the middle of the two packs. My buddies SV procs,,,he says run. I spirit walk back in his direction and we both face the packs from the front. We eventually kill them and move on.

Time invested in our characters, gear, paragon levels etc was all on the line - It's like riding a roller coaster. Yes, it's just a game but it's the biggest thrill in a game you'll find.

That's why I play Hardcore.