ACT and DBT could be considered sister/brother technologies. Both have been described as part of the "third wave" of cognitive-behavioral therapies, which also includes therapies such as mindfulness-based cognitive therapy and integrative behavioral couples therapy (and potentially the new modern behavior analytic form of behavioral activitation by the deceased Jacobson and colleagues that seems to be outperforming cognitive therapy for depression in two trials). This new set of therapies, all of which have a commitment to empirical evaluation and science, tend to differ in important ways from traditional CBT. For example, the third wave tends to pay more attention to secondary change in the area of thoughts and feelings. Traditional CBT tries to help people directly change thoughts and feelings, sort of an in-with-the-good out-with-the-bad approach to cognitive and emotional content. These third wave approaches focus on helping people to change their relationship to these private experiences, rather than trying to change the form, situational sensitivity, or content of these experiences. Emphasis then tends to turn to being effective in one's life and away from working to feel GOOD. Another way to put this is that these therapies tend to help people learn how to FEEL good, rather than to try to feel GOOD. Anyways, there are papers written about this new set of therapies and their similarities and differences for those who want more info.
Here's a little about what I see as differences/similiarities between DBT and ACT, with the disclaimer that I am far from an expert on DBT. DBT and ACT both emerge from a behavioral tradition. Both share the similarity of emphasizing acceptance, mindfulness, and effectiveness of action. In at least those domains they are quite similar. In terms of the theory that underlies them, they are quite different. ACT is closely tied to a modern behavior analytic theory of language and cognition called Relational Frame Theory (RFT), which underlies the approach, and also to traditional behavior analytic principles such as reinforcement. The first clinical trials on ACT were published several years before DBT (in 1985-86 with depression), but then Steve Hayes decided that ACT needed a firmer theoretical foundation and this lead to about 15 years of research and dozens of studies on RFT before the next application of RFT (an ACT clinical trial on psychosis) was published in 1999. My experience with DBT is that its focus has been on developing a technology that is practical, pragmatic, and manualized, with less of an emphasis on developing a comprehensive theory of human behavior. ACT is very closely tied to the broader tradition of behavior analysis and could be considered a form of clinical behavior analysis while DBT seems to be more closely tied to traditional behavior therapy.
In terms of overlap in specific techniques between ACT and DBT, the overlap appears limited. There seems to be very little overlap in terms of the specific techniques, exercises, and metaphors used in session (with the exception of general mindfulness exercises).
In terms of the evidence base, DBT undoubtedly has a stronger evidence with more replication in the more limited areas that it has been tested (e.g., parasuicidality/substance abuse), while ACT has been examined in a wider variety of clinical trials, with less replication, with more disorders (e.g., chronic pain, substance abuse, depression, workplace settings, anxiety, and a dozen or so other), probably due to the broader scope of its underlying theory.
[this is exerpted from an email to a listserv in Oregon and I thought others might be interested in this. Feel free to modify or comment on any disagreement/inconsistencies/extensions]