Dessicated thyroid preparations contain a variable amount of thyroid hormone. There are at least two different types of physiologically important thyroid hormone in the body (T4 and T3). T3 is really the hormone that is the 'active' hormone (the one that actually has effects in the body). T4 is sort of a resevoir hormone, meaning that T4 is converted by the body to T3 on demand. This is the main reason why T4 (synthroid, levothryoid, etc) is the preferred preparation for thyroid hormone replacement. It enables the body to adjust to the level of T3 needed at any time (second to second) by pulling on the T4 as needed. T4, as a resevoir hormone, has a long half life in the body (one pill's effects can be seen for 7 days), whereas T3 only lasts hours in the body. It is possible to just take T3 but you would have to take it around 3 times a day to be sure you were getting enough.
Long story shortened: Dessicated thyroid preps contain a not unexpected variable amount of both T4 and T3. There is no standardized method for quantifying the amount of either component so each preparation will be different than the next. Clinically, I doubt it would it be possible to tell the difference between taking synthroid (pure T4) and dessicated thyroid. In fact, cross-over studies of this have not shown that people can tell a difference other than by blood tests. Blood tests can be difficult to interpret with dessicated thyroid preps for the above mentioned reasons. This can lead, theoretically, put some people at risk for over treatment at times (risk of cardiac arrythmias and bone loss).
That all being said, treat the individual. If someone doesn't feel "right" on traditional preps like synthroid, etc. it would seem reasonable to try non-traditional preps as along as the risks (As mentioned above) are explained. Clearly, if some fails to see symptomatic improvement with a dessicated prep then I would stop it and start looking for other reasons.