The vinyl won't shine like paint (well, not like gloss paint anyway, more like a satin finish). I personally don't care for glossy stripes on cars (except the hood and trunk double stripes that run length of car). I think the satin finish adds a nice contrast in texture, as well as the color.
That being said, if I painted stripes on, they would be satin in finish anyway. But to each his own. But paint is more or less permanent (or at least a ton of work to alter), whereas vinyl is much easier to replace. Durability wise, I can't provide too much comment. I have seen numerous 1970 era cars carrying the original stripes at car shows, so they could hold up just fine. But if your car sits outside in the sun and weather, with bird dirt landing on it and such, paint will probably hold up better.