As yonder said Hardcore health allow for use of too many one hit weapons which discourages skill. For example one sniper with a m98 can cover a whole region in HC while in normal that would be very tough. Also weapons in bf3 are balanced more towards normal due to the damage per bullet. Those who argue that a sniper should be a one shot kill regardless should remember this a game not real life, balancing classes is essential. In the end if you have a good shot, HC or normal shouldn’t really make a big difference to you, your always aiming for the head anyways.
In regards to skill, yes normal takes more patience and you have to be sure of your shot. While it may look like in normal its takes way longer to kill, when you are playing against top teams, even normal health seems less. With even 100% health, making a mistake can cause you your life in a fraction of a second. Normal may let you get away with things at the lower comp level but at the highest level, it really makes no difference.
HC is fun as well and there are some tournaments that run HC ladders but they are never popular. I used to like HC as well but just the sheer amount of team killing in public server discourages me. A yonder said comp setting only have 100% from normal, everything else is essentially HC.
I recommend a balance between HC and Normal, HC gets you in the habit of watching your shot to make sure you are not killing friendlies which is very important in competitive and Normal gets you used to 100% health.