Another reason to paint is if the quality of the item is poor or cheap. Your's are neither so I would not paint them.
Do a basic web search for "shabby chic furniture finishing" and you will get a couple of pages of responses. Look for the ones that have videos or show step by step photos. You could also do the same search on You Tube for the how-to videos. I think that if you could find the right instructional video, the white and gray washed look would go well with your room. Good luck and I hope this helps.
I would paint.
I have two nightstands that I am torn between painting and staining. I've been told to stain because it will match my bed, which I have stained a dark kona color. It's beautiful, I love it. With the nightstands I feel that if I stain them the same it'll over power. So I'm considering a grey based stain, if I was able to sand them way down. I've also been told to paint them white. Which may be really nice and might also brighten the room but I would hate to take away the grain of the wood. Keep in mind I'm going for a beach theme and really would like to choose a color that would go well with it. I'm thankful for any help!