I am not a big fan of hardcore, I just find it too easy. You barely have to worry about how you fire your gun or even put much effort into aiming as the person you shoot at dies so quickly. To make it more fun I usually end up running around with the 1911 all or a good portion of the round. I do enjoy playing a few rounds of hardcore every now and then, but not my game of choice.
It's all about instant precision and reaction times.
Regular mode is like that to a large degree, but it's more about consistent precision more than anything else. If your first shots are gravy but fourth, fifth shots see you missing due to a bad reaction to recoil, you are probably done if the other guy is more consistent (even if you got a few rounds on him first).
Personally, while that is a good challenge in of itself, I dislike the ridiculous of requiring someone to consistently put that many rounds down range onto the same target.
Firefights against well-trained troops requiring skilled aiming, but more importantly, if both are skilled, having the first rounds strike the target before return volleys come your direction.
If skill is equal, it's purely about reaction time and consistency for a few rounds, or controlling recoil through an auto burst (start low, ride recoil up the target is a good burst method). But you can still pull off a kill if you react late (and they fire first) if you have better aim, or more importantly, are able to place rounds accurately (like on the head).
Plus, hardcore has the added bonus of removing icons. Granted, it kind of comes down to "don't aim at the ones with blue triangles, but aim at the ones with no triangles" - but I imagine a few servers out there even remove the friendly IDs (or... not?). There still a few oddities with that, of course.
Plus, unless you don't care about teamkilling, you have to be more careful when aiming into a group of soldiers. A friendly might be mixed up in there, or was making the move there - or stray fire at an enemy in the middle of an area is heading toward a friendly perched across the way. And the issue of "blind grenade tosses" and throwing mortars/rockets/other explosives to any particular point on the map and having a friendly wind up eating them. Oh, and of course the fun retards who run in front of you, while you are actively firing.
I had one person do exactly that, then "!punish" me as a result of the TK. I was like "dude, you're retarded". I rarely punish TKs because most often I know it was either entirely my mistake or a gamble on all our parts.
In short - I like it because it's slightly more "realistic" but I also don't strive for 100% authentic hardcore reality in FPS games. Very close is good, but authentic just gets tedious.
In some aspects of BF play, it is more entertaining and both more/less challenging to play in regular mode. I prefer regular for vehicular combat more often than not. Sure, being restricted to in-vehicle view only (hardcore) is a nice touch of realism (3rd person vision would be just grand, though), but with the chaos of 64p servers and friendly/enemy mixed in everywhere in a mostly unorganized chaos, it actually makes it more challenging than it even ought to be. Third person view gives you a good chance to view the randomness occurring all around you, and react/plan accordingly.
And it's also extremely awesome to see the 3D Spotting triangles way off in the distance or mixed in through the streets when in vehicles.