I believe that both of these responses can be valuable when handled correctly, but doing so requires a different strategy for each. Actually, the first step is the same for both: make sure that you've had the correct response: if you're sad, double check the criticism really is accurate; if angry, double check the criticism really is wrong. I think perhaps a lot of trouble can be attributed not to having one of these upset responses, but to having the wrong one! A helpful side-effect of thinking about the other kind of response is that they both mediate the other: thinking about situations/new evidence in which one might respond the other way to the same criticism alleviates the original emotional response.
The next steps are more involved and specific to each response but this comment is already longer than I meant it to be :).