Comparing phylogenetic models with different datasets
The key issue is the data is subject to reticulation, languages are seldom clean breaks. In nucleotide data this can be identified due to deviations from physical linkage and call it recombination. Linkage doesn't apply to languages.

The fundamental assumption is one tree - the same tree - describes all the data, with reticulation that may not be a good assumption. Thus English is a hybrid language, and lots of English words find their way back into French and German 'parents'. Or perhaps a better example is Gaelic mingles with English over time. There are methods used to monitor reticulation in languages.

Thus id keep it simple. The branch length is not only directly comparable it provides linguistical information that is useful to understand. This is the amount of 'evolutionaey' change per word (it that is what you binary data is describing) and the relationship to the node ('breakpoiint') is of primary interest.

The second step is to simply draw a tree of data set A and compare it to data set A+B and data set B and the probabilities describing the sister groups. Are the trees congruent, i.e. are they statistically the same?

The area you describing is more given to parametric bootstrapping, using custom resampling, but you need to be certain that the model being used is appropriate for the data.

The final point is whether a reversible or directional matrix is being used, which impacts on the specific result.