- Why more dangerous: A 1g steel ball is around 1/4 inch in diameter. A 1/4 inch hole in any major artery is an immediate life-threatening event, same if it hits the lungs, heart, or brain (gut-reaction: I think it'd be quite hard to penetrate the skull with this projectile, so to hit the brain you'd have to go through the eyes or pterion or something, but ignoring that sort of potential quibbling). It'll have pretty significant negative effects on any other system if it can actually pierce that system. If we pick a denser material like lead, the hole is smaller but still life-threatening. If we pick a less-dense material like wood, the hole is larger, and you're still pretty majorly screwed. Contrast that with the 1kg object, which is roughly equivalent to dropping two cans of beans from a height of 2 inches; it just doesn't matter.
- Why pierce: That's a big can of worms with a lot of answers. A halfway okay way to think about it for common hard materials and common shapes in the speed regime being discussed is that you have a higher energy to surface-area ratio.
Critically (in case you're using some sort of Socratic method to guide me to the increased energy being the rationale), the important number for piercing injuries is closer to being that ratio than the total energy, hence my example of 1mg at 1km/s in some recent comment. That has the same energy as our 1kg at 1m/s object, but it's still extremely dangerous because it physically punches out a 1mm hole through your body. If that strikes a location like your eye or a superficially exposed major artery (like the one on the inside of your elbow), you're still going to have a very bad day.