This is not a bad question at all.
When building for softcore- I tend to put more stat points into dex and str- to be able to twink and test gear combos etc. faster. Also- I tend to care a bit less about resists and blocking % in SC.
Now in HC- different story all together. Resists, Blocking %, Damage reduction, walk & run speed, faster hit recovery, attack frame rates, defense numbers, all that becomes much more critical. I also want more damage per attack with the Hardcore characters. Simply because I want things dead FAST so I don't have to worry about them. Get ready to put all points that aren't needed for equipment and blocking into vitality.
I also put WAY more emphasis on poison damage augmentation and ranged weapons (on the switch) on my HC's. That way I don't have to be right on top of something to kill it (like FE's and CE's). Learning to kill from a distance with poison and ranged weapons will save you ALOT of grief.
Any build that can thrive in HC can thrive in SC- but the same can't always be said for the other way around.