I don't think it really matters - in my experience nobody has ever taken offensive to me saying I'm vegan for ethical/moral reasons, or that I think it's wrong for people to eat animal products. Most grown up adults know that different people have different ideas about what is right or wrong, and just because they do something you don't believe in/agree with, doesn't mean it's a personal affront or judgement on them.
For me, adding the "personal" is too close to the "it's a personal choice if somebody wants to use animal products" idea which really isn't what I believe in. I believe that for the vast majority of people, it's wrong for them to use animal products. I don't think there is anything wrong with saying that. Personally I'll only say that specifically if I am asked, but often people do ask because they're curious, and I've never had someone offended by what I've said. What I usually say when asked why I'n vegan is "I believe that I shouldn't cause animals to suffer if I don't need to, and since it's easy not to and I don't need to, I don't" or something along those lines.
I think a lot of people worry unnessersairly about how people will react to them being vegan. Most people are just curious - what do you eat? have you always been vegan? are your parents vegan? do you think you'll always be vegan? etc. Just be yourself - you don't feel the need to question exactly what words you use when you talk about your other oppinions or beliefs or ideas, so why do it with veganism? There's this big emphisis on being a GOOD VEGAN in the (online) vegan community, as if we're all walking talking one person adverts for veganism 24/7 - I think it's really silly. We're just people, just be yourself.