It sounds like what you're after is testing measurement invariance. To do invariance testing, you might start by checking that the given factor model fits well in both samples individually. You could then perform multiple group analyses, where you sequentially apply constraints - starting with applying the same general factor model to both groups at the same time, then you might hold factor loadings to be equal across the groups, then both factor loadings and intercepts, and so on. This will give you an idea of the extent to which the factor model is invariant across the two groups.
A caution, though: a model with approximately 11 items per factor is inevitably going to do poorly on some CFA fit statistics, especially the model chi square (which tests a null hypothesis that the model fits exactly in the population(s) of interest). In effect the problem is that you're expecting a relatively simple model to do an awful lot (explain the covariances between a lot of items - 1540 covariance terms in all!) So it's good to start thinking about whether you're willing to accept a model that might fit the data "reasonably", but not closely.
One alternative to CFA could be to run EFA in both samples, but with a strong pre-selected criterion for how many factors to select. Parallel analysis or Velicer's MAP are better ways to determine the number of factors than the usual methods such as Kaiser's stopping rule or a scree plot. If the same number of factors is extracted in both samples, and the same items load on each factor, this supports the validity of the model across both samples. (This would be an unconventional way to go about dealing with this problem - just an idea).
lavaan package in R. It's free, allows adjustments to fit statistics for breaches of normality (AMOS doesn't), and has a great measurement invariance function which automatically takes you through several steps of invariance testing (invariance testing in AMOS is quite time consuming). On the other hand AMOS allows you to specify models purely using a graphical user interface and path diagrams rather than code or syntax, which does make the learning curve a bit flatter.
As to how to actually run the analysis, the best thing is to look at the user's guide of the program you decide on and have a play with a program.
To help with this question and your analysis in general I'd suggest getting hold of Confirmatory Factor Analysis by Timothy Brown. As far as I know it's still the only book specifically focused on CFA, and is very readable and helpful.2. How to interpret the results of the CFA to determine whether the factors were identical and the extent to which they differ.