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.
I have "gloss" stripes in black over Hemi Orange - the stripes have a satin/ semi-gloss look vs. the high sheen of paint.
Vinyl - the pros are that if a stone chips the stripe, you can replace the stripe very easily and be back to the way it was before the damage. If you change your mind, you can un-do the look pretty easily.
Vinyl - the cons are that for cars that sit outside, the material will age and degrade over the years. Car washes and high pressure washers are not recommended as this can cause the adhesive to fail.
Paint - the pros are you can get a high gloss to matte finish if you desire with paint. The maintenance is easier, since you are dealing with a painted surface.
Paint - the cons are if you get a stone chip, the main body color may show through and it will require re-finishing or touch-up to repair the damage and that costs more.
I've had 10 - 16 year old cars that had vinyl stripes that held up very well with proper care still looked good, but this is dependent on the conditions and level of care the owner subjects the car to.