Plywood and OSB (Oriented Strand Board) are popular sheathing materials in wood- construction.
They provide structural strength to walls and roofs, and provide a nail-base, but they are prone to moisture problems.
Plywood vs. OSB
Standard OSB is cheaper than plywood. But is it the best choice?
If your alternative is between OSB and plywood, unless you live in a dry climate, consider plywood (or premium OSB products).
They are slightly more costly, but plywood and premium OSB worth their price; they are more resistant to moisture (even if marginally) and more stable and durable.
For a more extensive comparison between OSB and plywood, see this Amherst University document.
Structural sheathing water-resistant products
Structural fiberboard and diagonal board sheathing over OSB reduce the risk of rot in walls and ceilings.
They are more expensive but also more moisture-resistant than plywood or OSB.
Other “Traditional” sheathing alternatives
Traditional sheathing alternatives to plywood and OBS include products such as common fiberboard, cementitious board, fiber cement, foil and paper faced insulative board and wood and gypsum boards.
Some of these materials may have some distinctive advantages over OSB or plywood, but on the whole they aren't as flexible, or as easy to apply or as inexpensive as OSB and plywood.
For a brief description of these materials and their manufacturers, see this Toolbase tech note.
Plywood, OSB and water moisture issues
Sheathing rot is a major problem in wood frame construction, and if you are going to build a new house you should take it into consideration.
The type of sheathing matters, but only marginally.
There are more important features to consider. To prevent sheathing rot you have to act upon the 1) causes behind the penetration of moisture in the exerior walls and... 2) to increase the ability of the walls to dry. You have to keep moisture out of the walls, as much as possible.
Tot get it, pay attention to
1) flashing issues around windows and other wall penetrations;
2) build a good rainscreen between the siding and the sheathing;
3) get the details about water resistive materials/barriers (WRB) right;
4) consider capillary breaks and a good siding and...
5) do not underrate the first lines of defense of the walls: large roof overhangs and good drainage.
If you live in a cold climate, you should also pay attention to...
1) foam sheathing issues,
2) the thickness of the wal and
3) the type of insulation.
Foam sheathing (that is, a continuous layer of insulation over the sheathing) is critical to reduce thermal bridging (heat transfer through the walls), but it also allows to keep the sheathing warmer, reducing the risk of rot. Just make sure that the foam is thick enough; a very thin foam layer will not warm the sheathing enough and will reduce the ability of the sheathing to dry to the outside.
The type of thermal insulation in the wall also matters; fiberglass is air-permeable, which is a problem in leaky ceilings and walls. There are better materials: dense-packed cellulose, mineral wool, or other non-air-permeable materials... They will reduce the risk of moisture condensation (by lowering air movement through the insulation).
But you should also considerer the thickness of the wall, unless you don't live in a cold climate: the sheathing in thick walls tends to be colder during the winter, and cold sheathing has an increased ability to accumulate moisture.
This issue is especially important in energy-efficient homes, with very thick walls. That's the case of double 2x4 walls: without a proper design they create an increased risk of water and moisture condensation damage (unless they include a well-designed ventilated rainscreen to allow drying).