On the scientific base... well, there are what they called "evidence-based" treatments. Mostly on the cognitive approaches that are more structured, such as CBT. This guy has written papers including some scientific type analyses on psychodynamic therapy:
writings | Jonathan Shedler, PhD

Collecting data and analyzing it is quite difficult for a variety of factors, e.g.
-the population of people that provide feedback is usually very biased
-hard to follow up, once clients leave, usually they don't care to go back and report
-the data are based mostly on self reports
-what would be the criteria of therapy working - very hard to define universally
-the usual limitation of clinical mental health studies: cases are not hard to find but who will be the "healthy controls"?
and a lot more. But there are many so-called studies published, usually not in very high profile science journals.

I do research on mental health for living (mostly basic science rather than clinical) and I am most definitely not convinced about the scientific evidence related to the efficacy of psychotherapy. The government in the US has definitely reduced funding in the past few years even for hardcore mental health-related research and it does not look more promising for the coming years either.