Generally speaking the more falsifiable a theory is the better a theory it is. This is for the reason that the more a theory claims, the more opportunities exist to find observation statements that are inconsistent with it. Theories that make wide-ranging claims are considered to be epistemologically more desirable than those that don not (assuming they have not been falsified). Science aims at producing theories with large information content.
Example:
Note: Clearly Law (2) would appear to have higher status as a piece of scientific knowledge because it explains a generality in celestial mechanics. Consequently the second law is more falsifiable. Further any falsification of the first law will be a falsification of the second, however the reverse is not true.
``I can therefore gladly admit that falsificationists like myself much prefer an attempt to solve an interesting problem by a bold conjecture, even (and especially) if it soon turns out to be false, to any recital of a sequence of irrelevant truisms. We prefer this because we believe that this is the way in which we can learn from our mistakes; and that in finding that our conjecture was false we shall have learn't much about the truth, and shall have got nearer to the truth.''
Karl Popper (1969) (italics in original)