My own prejudice would be to analyse the two data sets separately, even if you decide to concatenate them afterwards. That way you can see if they have compatible information content. If they dont, mixing them will produce a meaningless result.
I agree with Peter. Different (but incompatible) datasets coud provide information at different levels of the tree, producing a beter result. Doing individual analyses for different genes, and morphology, is ignoring the total evidence concept. You can explore the data, to check if strong evidence of incompatibiliy arises, that could be originated by a non-phylogeny related phenomenon (e.g. horizontal transfer of some gene). But if you don't have strong evidence of such thing, doing a partitioned analysis is not logical. Imagine a dinosaur dataset, bout you choose to analyse head characters separated of the others because appears to be "incompatible"... Does this have any sense? Morphology and genes are all characters from the same organism, and have to be analyzed together.
I am familiar with arguments for using "total evidence"- nowadays this usuallly means mixing morphological and molecular data. The problem I see is the relative weighting of the two totally disparate characters. Do the male genitalia characters count the same as each nucleotide position? Or ten times as much? Or ten times less? Given enough time and effort, you can come up with any result you choose by tinkering with the weighting, if the two data sets are saying different things. Perhaps illogically, I dont have the same deep distrust of using Total evidence if it just means concatenating different genes. I do that all the time!
OK, Peter, I cant imagine myself in quite the situation you describe, but should it occur I would combine both data sets. Then I would explain why I distrust one of the data sets, and present the results obtained from each set separately. Wouldnt you?