If your goal is to compare the part-worth utilities (preference scores) between countries, then (the Bayesians would argue) HB analysis with a covariate set to country membership is a very strong approach. You compare the history of "alphas" for the used draws associated with the covariate (saved in an alpha file separate from the utility estimates) and count for what percent of the respondents the country covariate for a particular parameter is larger or smaller than for the other country. We describe this process in the paper found at: https://www.sawtoothsoftware.com/download/techpap/HBCovariates.pdf
Frequentist folks would simply take the final utilities (point estimates from HB) for the two groups of respondents, and after normalizing using zero-centered Diffs (you can export these to this normalization using SMRT's Analysis + Run Manager + Export), using t-tests or F-tests to compare the two groups on the utilities.
Now, if your goal is to test whether the two countries have the same segmentation structure, then that would seem to leverage Latent Class analysis. Your suggested approach seems intuitively nice, but I don't know of a formal statistical test of whether the segmentation structures are different within a country vs. the pooled countries. Maybe somebody with more expertise in Latent Class can comment on that.