Eddie. Here in the PNW our buildings are subjected to a lot of rain before getting enclosed. For a litttle she shed I am building for the wife I chose Plywood due to bad experience with OSB in the rain before (1996 OSB). Has it changed enough to withstand prolonged exposure to rain (2 weeks worse case?) The plywoood we got wasn't that great this time around, seems like wood just isn't what it used to be. Also, would you consider OSB for inside wall paneling for a shop?
Both plywood and OSB are going to have their issues if enough rain gets to them. For more money, there is nothing that compares to Zip Siding if you are going to put something over it for exterior siding. If you are just building a shed, you might want to look into Smart Siding. Both are very high grades of OSB. They are denser, heavier and they cut smoother. Once you've worked with both, it's very obvious how much better quality they are.
Smart siding is kind of like T1-11 in appearance and function. The long edge has an overlap for a clean seam, but the finish side with the wood grain is a kind of hard plastic something or other that looks like wood, but isn't. Paint sticks to it forever unlike T1-11 plywood. You don't put anything under it, you just attach it right to the studs and you are done.
If you are going to do something like Hardie Lap siding, or just about anything else that you will be covering your sheathing, but it's not going to happen quickly, then Zip System has a special coating on it that keeps the wind and water out. It also comes in different lengths. 4x8, 4x9, 4x10 and 4x12 are all sizes that I've bought and used. You tape the edges with their Zip Tape and that makes the entire area water tight. The reason I use it is that I'm slowly redoing the exterior of my house one wall at a time. Since you tape the edges, there is no stress of what will happen if there is a storm. Once it's up and taped, nothing is getting past it. Then when I have time, I install the Hardie. The side of the house where I'm building my Akita Pool and new porch has had the Zip System up for several months and will hopefully get covered in Hardie before the end of the year, but if that doesn't happen, I'm not worried about it. The other side of my house, where I've added on to my house 12 feet has had the Zip System exposed for three years now. Might be another three years before I'm ready to finally cover it up.