Oh man. This is a difficult question.
Firstly, the specific answer to to why E,Z is more soluble to Z,Z.
http://en.wikipedia.org/wiki/File:Bilirubin-from-xtal-1978-3D-balls.png <-- This picture is the Z,Z structure. If we were to rotate one of the ends, then we completely change the molecular structure. This increases solubility, some may say it is because more polar groups are exposed, the mechanism of dissolution is still under debate at the moment.
The more general effect you are talking about is 'photoisomerization'. I don't know how or why it happens. I remember going to a guest lecture a few weeks ago, where the guy was talking about excited state quantum calculations or something, and presented his results which he claims to predict photoisomerization. Essentially, in an atom, electrons absorb light, jump up energy levels, then release light and jump down energy levels. In more complex systems, electrons absorb light, but the system can relaxes via some non-radiative mechanism, which involves some structural changes, so the energy absorbed from the light is expended in the cis-trans conversion process. Bonds aren't broken in the process, the electron density simply shifts around a bit.
As for how to predict if this will always happen, what wavelength of light is needed, what isomer is more favourable, and so on, I don't think there is an easy theoretical answer, or worse, there might not be an answer at all.