At about 15 to 30 bucks a gallon for paint, it doesn't take much to make up the price difference to a marine grade of plywood that will last years and years without any paint. I never liked OSB as I always found that small pieces always de-laminate and turn into large splinters ready to injure you.
Home Depot - Marine plywood 3/4" $70 ON THEIR WEB SITE
OSB - $15
BUT TRY TO FIND MARINE PLYWOOD!!
I wanted to use marine plywood for building some boxes that I plan to use to haul stuff for decades. In Northern Virginia NONE of the regular lumber yards OR the HD's or Lowes would order it. And I called several marinas. I found one "specialty" shop, referred by a marina, that sold it - $110/sheet! And that was if I ordered 5 sheets.
I have to agree with Gary the Marine plywood is the way to go.
IF you can find it!
I've seen OSB scrap get ruined by rain in a few weeks. On the other hand, I have had regular old 15/32" plywood side boards on my trailer for 7 years now. It turned gray, but is still holding up OK and functioning fine. It was scrap, so I figured no big deal if it only lasted a little while, but it's far exceeded my expectations.
By the time you paint/treat OSB, you may as well have gone with plywood to save time/money.
PT plywood will last for years with a little paint.
I've built a lot of stuff with PT plywood that lived outside with minimal protection, 2 layers of WHOOPS paint, seal the edges, lasts for years. I tried OSB with the same treatment. But with OSB if you get a break in the paint ANYWHERE it just sucks in moisture and delaminates. Nail, screw holes are the worst. With a little normal flexing you get a hole.
I'd say use marine plywood IF you can get it at a reasonable price. PT with a little maintenance is good, OSB requires a lot more careful maintenance.
Now if ANYBODY knows where I can get a good marine plywood near Alexandria Va. for <$70/sheet of 3/4" x 4' x 8' I'd like to know.
Until then I'm stuck with PT at ~$40/sheet.
* WHOOPS paint is the stuff you find at the hardware store for $3 to $5/gallon because someone returned a tinted can