Husquvarna has had birch stocks for years in their generic firearms. I've always considered the Husky name to be one of the top in the firearms industry so if its good enough for them, its OK Fine with me as well.
As for the differences, birch is much lighter in weight, finer grained than walnut and of course, lighter in color. As long as the grain is straight w/o knots, the birch will hold up fine.