The paper does not give it strength. The intended purpose of MDO is for signs and exterior painted projects. The reason it lies flatter and stays flatter is due to the core.
Plywood comes in many faces and cores. The key when looking for good plywood is determining what the core is. In most Big Box stores, you'll find that the core is cheap Chinese plywood with a nice face. In building a table that will be covered, the face means nothing. A quick way to see this is the number of plys you can see on the edge - lots of thin little plys generally means low quality plywood. Full of voids and holes - this is what causes the sheet to warp when cut or machined.
If you can find Baltic Birch in 4x8, it will likely be the flattest and most stable plywood at a reasonable cost.
OSB is by FAR more rigid than a comparable thickness of plywood. It will be significantly heavier though. If you want to get the best OSB, try to use an enhanced OSB (Advantech, Point 6, Edgegold, etc.). They will all hold a screw just fine.