On my shed, I tried to paint both sides, to seal it. I also attempted to caulk the edges. No avail, it still delaminated in a spot. But, it's a metal shed, and the edges are exposed to rain and snow (shed can have a few feet of snow on it, one driveway dumps snow onto it, plus whatever I pull off the roof). I recaulked it, nailed it down, and, well, it's a shed. But I wish I had either gone for 1/2" plywood (instead of 3/4) or something rated for more moisture.
I'm not sure how much wood has to breath, but I'm going to guess it'll last longer with paint on both sides. Seems like any trim board on houses that I've seen, where they only paint one side, still gets a fair amount of aging on the unpainted side. It might not get soaking wet but it still sees the humidity.