I like button downs a lot more. I'd probably take the guy in a button down more serious if he approached me, hate to say it. There's nothing wrong with a graphic tee, but wearing one when you're first meeting a girl might not give off such a good first impression as the button down.
i like the button down better.. even if it was a button down over a tee it looks better than just a tee.. a tee is very ordinary and not really trying to look nice.. I like a guy to try to look nice at least when he goes out.. that might just be me but ya.. you can't go wrong with a button down ;)
I personally like button downs but not all the time. I like guys wearing t-shirts, athletic shorts, graphic t-shirts (as long as they don't have inappropriate stuff on them), button down shirts, jeans, khaki pants, polo's, sweat shirts, vests, etc.
They're both fine, but I recommend the button down/sportshirts. I just think sportshirts make for a more sophisticated and mature look.
I have some of these... link I recommend solid or striped, though I may sooner or later venture into plaid, of course depending on the shade. You can always wear a graphic tee under these too. I used to wear just white undershirts, but started moving into wearing t-shirts underneath. Not a bad look at all if you ask me.