I am not interested in starting a flame war, however it is reasonable to expect that posts have some relevance, and be factually correct. So let's set the record straight on the significance of shear strength AS IT PERTAINS TO DEFLECTION of a structural element, which is what we are talking about here.
The deflection of a structural element under bending load (we are talking about bending loads here, because the element we are discussing is a horizontal beam or joist loaded along the length of the element) depends on the following factors:
1. The moment of inertia of the element. The greater the moment of inertia, the lower the deflection. Moment of inertia increases as the cube of the depth, and is linear with the width of the element.
2. The modulus of elasticity of the element. The greater the modulus, the lower the deflection. Steel has a modulus about 20 times that of wood, therefore a steel beam of the SAME SHAPE as a wood beam will deflect approximately 20 times less than the equivalent shaped wood beam. This is a discussion about deflection, NOT strength.
3. The load. The greater the load, the greater the deflection. In this case, we are comparing structural elements under identical load, so this factor does not come into play.
So let's see what this tells us. If you take a sawn wood element like a 2x10 and uniformly load it, you will get maximum deflection at the center. If you strengthen this element by sistering another 2x10 to the first one, you will have doubled the moment of inertia, and the deflection will be half that of a single element, under constant loading. If you attach another 2x10 to the bottom of the first 2x10, making effectively a 2x20, the moment of inertia is now 8 times as large, and the deflection is 1/8 that of a single 2x10.
The kicker is that you will have a much deeper beam, and you need to glue and/or nail the second 2x10 onto the first adequately so that you carry the full amount of horizontal shear generated at the interface. This is HORIZONTAL shear, not vertical shear. If you do this, you get a composite beam with 8 times the moment of inertia, and 1/8 the deflection. Again, this is NOT a discussion about strength, merely deflection.
If you nail on a piece of OSB which is 1/2 inch thick and 9.5 inches deep to the side of the 2x10, you will increase the moment of inertia of the composite section by approximately 1/3 (1/2 inch is 1/3 of 1.5 inches, the presumed width of the 2x10). Assuming the modulus of the OSB is approximately the same as that of the sawn lumber, which it usually is, the deflection will be approximately 1.5/2 = .75, so there will be a 25% decrease in deflection. You get exactly the same result if you nail on a 1/2 inch thick x 9.5 inch thick piece of plywood or sawn lumber, assuming the modulus of elasticity of the nailed on piece is the same as the lumber, and it is usually close. This assumes you use an adequate number of nails and/or glue to resist the horizontal shear induced by the composite action of the beam under load.
Note that in this discussion of deflection, the issue of vertical shear has NOT COME UP. Vertical shear almost never controls in residential construction, and it is therefore irrelevant in the case of deflection how strong plywood or OSB is in vertical shear (vertical shear is normally just called shear), therefore Bud is exactly correct, it makes no difference for this discussion how strong in shear OSB is vs. plywood. We also had no need to discuss strength to determine deflection. In the real world, the engineer designing your beam always checks the structural element for strength and deflection, and sizes the beam based on the more restrictive condition.
Conclusion: It is perfectly reasonable to stiffen a beam or joist by nailing/gluing on plywood, OSB or sawn lumber. It is more effective to attach the new wood to the bottom of the existing beam, but this is rarely done because of the difficulty in getting adequate attachment to the bottom to resist horizontal shear. The most effective choice would be the product with the greatest modulus of elasticity, however since they are all about the same, the grand conclusion is it makes little difference which type you use.
Note: You need to do some deflection calculations before you go nailing or gluing to your existing joists, since you need to know how thick an addition you need to make.