I remember that Taiwan had severe issue concerning the topic of your question. I came across the attached publication which tackles aspects of rainfall induced landslides and a major earthquake. Hope that helps...
Article Impact of Chi-Chi earthquake on the occurrence of landslides...
If I understand, you are asking for the effect of eartquakes in rainfall-induced landslides (i.e. in already existing landslides provoked by high amounts of precipitation in a short time). Am I right? In this case, earthquakes can provoke re-sliding processes in the landslide scar or in its uppermost areas, subjected to strong erosion and geomorphological instability.
Anyway, there are "pure" earthquake- and rainfall-induced landslides, but I think that the difference among them is quite easy ;-)
In order to get more information, I suggest you to check the classic study of Garwood et al. (1979), or the more recent review paper by Restrepo et al. 2010, among other studies.
Get lucky with your query,
Eduardo
References
Garwood NC, Janos DP, Brokaw N. 1979. Earthquake-caused landslides: a major disturbance to tropical forests. Science 205(4410): 997-9.
Carla Restrepo, Lawrence R. Walker, Aaron B. Shiels, Rainer Bussmann, Lieven Claessens, Simey Fisch, Pablo Lozano, Girish Negi, Leonardo Paolini, Germán Poveda, Carlos Ramos-Scharrón, Michael Richter, and Eduardo Velázquez 2009. Landsliding and Its Multiscale Influence on Mountainscapes. BioScience 59(8): 685-698.
In comparison to the dry and wet state of geomaterial subjected to the EQ loading, definitely the saturated slopes are more likely to fail in the event of earthquake.
You can reproduce the situation in the element testing in Laboratory.
After making specimen, saturate it and apply the cyclic loading to see the response in stages.