Well for me, getting rid of dairy is a very good choice health-wise because it doesn't agree with me at all. I've been consuming dairy for years knowing it was bad for me and there's no telling what damage I've done to my body.

So soon after going vegetarian I started getting rid of dairy and it just seems natural to get rid of eggs too. I still eat them on occasion, but I'm finding them not-so-appetizing these days thinking about the conditions they come from. I took 2 bites of my eggs this morning and I was done.
So FOR ME I think veganism would be healthier. I understand about proper nutrition so I won't be a vegan who survives on potato chips and coconut milk ice cream (I'm sure vegans like that are out there).
I don't think one is inherently healthier than the other. It depends on your diet as a whole since certainly there are vegetarians out there that are healthier than some vegans. I'm sure there are meat-eaters who are healthier than some vegetarians. It all depends.
I think as a whole though, assuming everyone is eating well-rounded diets, vegans are going to be healthier unless the people eating animal products are super conscious of their saturated fat intake, plus where they get their food sources (because of hormones and antibiotics and stuff).