Lag affects both game modes equally. I don't notice a difference. That being said, HC kill confined for me is by far the best game mode. Dropped my first Nuclear and First Chainkill this week.
The problem with core is that this game is fast paced so the more bullets you gotta pump into the enemy the more inconsistent the game will play. I discovered this years ago and since switching to hardcore I have enjoyed this game. I play with family across the country and don't have nearly as many problems as I did when I played core, my internet is the best I can get here in my area and I don't see lag comp problems. HC is the best way to enjoy this game, too bad more gamers don't see the light.
I have been a HC player consistently since MW2 when the same issues I hear Core players complaining about this game plagued me in Core in that one.
People used to call me a "fanboy" when I told them I wasn't having the issues they were explaining, but the fact of the matter is.. HC plays better. Without the increased Health and Health Regen... you don't get a lot of the silliness Core players are having to contend with. It typically plays smoothly beyond the occasional bad host, and 9/10 the game migrates host in that case.
Welcome to the party.
After having played many, many hours of Core KC - and raging at all of the BS hitmarkers - I found out a few friends play HC TDM all the time and decided to join them.
Result: 99% reduction in rage. You shoot first, they die. They shoot first, you die. One, maybe two bullets with pretty much any gun, even at distance. Killing head-glitchers, much easier. None of the "I shot him with half a magazine in the back, only for him to turn around and drop me with one shot" garbage.
Is HC TDM more campy than Core KC? Sure, but many games still reach the required 75 points and there are enough RnG's from other modes migrating that keep most of the games moving.
I'll still play some Core KC, but when I do I'm instantly reminded of how much of a pain in the ass it is. I guess I'm the type of player that has decent reaction time and can hit with the first bullet, but not stay dead on target for 10+ while trying to avoid their bullets.
As far as the campiness is concerned? Or in another way? I suppose it's quite a risk going for your tags in HCKC. Definitely requires some forethought before running out into the open!
I think that HC TDM's reputation of being "more campy" is no longer deserved. While it is still there to some degree, especially on easy spawn flip maps like Slums, its much faster paced and fun than it ever has been.