Vegan is more ethical and you don't eat animal products at all.

Not trying to argue here, but you do know that cows need to be milked or they will develop mastites and other diseases, unless you don't take the calf away from them, but even when the calf is taken from the mother they are usually put somewhere they can see each other.
Still good for you to turn vegetarian, i turned vegan for 2 year, but my body didn't like that eating habbit very much, i workout a lot, i started having iron deficiency even though i hate a truckload of spinach, so i had to supplement iron, than i started having deficiency in b12, so i had to start taking a multivitamin, and my metabolism couldn't deal with the amount of carbs and less protein that i was ingesting, i started losing muscle and gain fat, my metabolism is really slow, so i had to quit, and switch back to eating meat, in a couple of months i lost a ton of fat and gained a lot of muscle.
Being a vegetarian is not for everyone, but everyone should try, because it is better for your health and the environment.

I turned vegan mainly for the same reasons you did, because i didn't like to hurt animals, that's why i'm studying veterinary medicine , and if i could be healthy without eating animal i would never eat another animal.