with the available 3M Di Noc films i would definitely wrap it. works as a bra and replacable as needed when worn.
with paint you have to touch it up or re-sand/paint and it will take a lot more work.
i have to say though, that the duplicolor engine enamel matte-black i used on my dd's fog lamp surrounds have held up VERY WELL to chips and weather (including salt). if i had no choice but to paint it, i would use that paint for sure.