I am looking for a method to use to test for equality of two cumulative density functions.
The QQ-plot and the Kolmogorov-Smirnov test are two widely used options. A QQ-plot requires some level of expertise, as the decision is based on your own judgement. See also the answers to this question for more discussion about both tests. I use there the Shapiro-Wilks test for normality, which can be seen as a parametric counterpart of the KS test in case the comparison is made with a normal distribution.
For reference, I'd like to point out the book Comparing Distributions from prof. dr. Olivier Thas. This gives a thorough overview of parametric, semi-parametric and non-parametric approaches to the topic.
Plot their inverses against one another, i.e. make a quantile-quantile plot:
Lately I've been playing with comparing distributions by computing the difference between their empirical CDFs and then bootstrapping intervals on this difference. Differences between the distributions in location, scale, and each tail all have different and rather noticeable effects on the DECDF function.