This is something that could be accomplished using a linear modeling framework, so limma might be a good tool to use. However, automatically determining the experimental design may be difficult. I do not know of an automated system for analyzing datasets of arbitrary complexity that does not require human intervention.

Edit: My assumption here is that we are talking about an experiment performed on the same array platform in the same laboratory, etc. If that was not the original poster's situation, linear modeling will be much more complicated (or impossible) given the known confounding effects of between-lab and platform biases.

Are the treatments in each experience roughly similar? If so, Sean Davis advice of using limma and simply redefining your factor matrix is a good idea.

However, keep in mind that experimental protocols (culture medium, extraction, amplification, microarray platform, scanner, etc.) can have a large impact on microarray results. If the protocols differ significantly enough, it might not be a good idea to perform a numerical analysis on a "pool" of both result sets. Generating two separate gene lists then comparing them would be a much safer and logical choice in that case.