Broiling typically keeps the juices in the meat. There is less chance of burning or oxidizing it, (unless you don't tend it properly). Left too long on broil, the meat will dry out. The fat drips out, so you are left with less saturated fat in the meat.

Some ovens have a broiler beneath that you pull out.

We use a tabletop broiler. I grew up with broiling so I just do it out of habit, but healthwise I think it is the safest way to cook some types of meat.

Charcoal grilling allows the burning embers along with the chemicals in the briquets to rise up and coat the food. While this imparts some flavor if done right, it also imparts, carcinogens.
Standing over the grill you breathe these in. Studies have shown that in Asia where people grill all day long in outside markets, those exposed to the grill fumes develop lung cancer at a fast rate.

I have an electric dutch oven too, for baking smaller meals on the tabletop. This seals in juices, and I used to do it for the time saving factor. But it appears to be a good way to cook too.
I throw everything in together and bake it (all kinds of veggies + meat). Taught hubby since it was simple, since I worked long hours. My grandmother used to make roasts this way.
We don't have a large family, so using the big oven seems like a waste to me.

I really cannot stand charcoal grilled food anymore...I can taste the chemicals involved. Gas is ok for me, but we only do it upNorth mostly because we don't have electricity there.