Being Vegan is quite extremely unhealthy to be honest. Vegetarians are usually healthy but often have diet related problems. Oh and for the record, being omnivorous is technically quite unhealthy too.
But it's quite problematic trying to find any statistical evidence for or against diets, as the golden rule of modern medicine is that the sponsor always gets the answer they want. So studies show whatever the people who paid for them want, i.e. the Atkins diet being healthy. So it's all just inane babble really that we can't answer.