I am going to preface this by saying I don't have practical experience with merits of birch stocks vs walnut. As a wood products person, however, it's my understanding that strength aspects of wood generally increase with density, rather than species.
Birch is listed as slightly denser than walnut, so raf is generally right. You need to realize, also that wood is a very non-homogeneous product, so I am sure that there are birch samples that are much weaker than walnut samples. Grain deviations such as burls etc, would also influence wood structural properties.
Unless you are planning on using your M-14 for bayonet work, walnut will be more than strong enough. Both walnut and birch are not dimensionally stable over different moisture regimes, so if you want stability and strength, you ought to go with synthetic stocks. You could also try laminated wood, but cellulose, the primary strength consituent in wood, has a chemical composition that ATTRACTS water vapor. Oils, finishes and the like will only retard this attraction.
As a person who has watched too many loads of plywood coming out of a hot press, I can say that even plywood, which maximizes wood stability, can be absolutely stricken with warp problems.
According to the Forest Products Laboratory "Wood Handbook,"
Black Walnut:
Specific gravity oven dry .55
Modulus of rupture 14,600 psi
Modulus of Elasticity (stiffness) 1.68 million psi
Yellow Birch:
Specific gravity OD .62
MOR 16,600
MOE 2.01 million psi
Again, these values are not set in stone; trees grow differently under different conditions.
And that is the real beauty of wood!! It's got the "nice linah!"