Before either site existed, I wrote:
Biblical Hermeneutics, as I've come to understand, turns out to be a very technical topic not dissimilar from programming (at least the debugging side) or historical research.
I am a Christian and I believe a general Christianity Q&A site will be very challenging to moderate because of the question of authority. To put it simply, not all Christian traditions rely on the same set of authority for answering questions of faith.
I was largely correct on the hermeneutics side. One of the most often referenced question on meta.hermeneutics is What are we looking for in answers? Like many questions on meta, it defines boundaries of the methods of interpretation acceptable to the community. Appeal to authority is heavily discouraged by community standards. The controversies in meta tend to revolve around whether posts deal with reproducible methods of interpretation or whether there is an implicit appeal to authority.
It happens I was hilariously wrong about how the Christianity site would work. (This is why I didn't quote the majority of my drivel in those posts.) I was more or less correct that answers would be grounded in authority. But what I failed to anticipate was that the early users of this site (of which I was not one) would use tagging to create scope for questions to be answered in. Yes, answers appeal to as many authorities as there are Christian traditions. But no, it's not chaos because good questions set understandable restrictions on answers.
The most often cited question on meta.Christianity is the provocatively titled Brothers, we are not Christians‼ The idea is that users must check their tradition at the door (unless they happen to be asking or answering questions in that tag) for the good of the greater community. Users might find themselves writing answer they personally disagree with when answering questions from the perspective of some other viewpoint. Answers on Biblical Hermeneutics are more likely to reflect the views of their author which need not be Christian.
A lot of the work of answering on Christianity consists of gathering evidence and interpreting it. The most often cited meta BH meta question is What texts are open for examination? So one way to look a the difference between the sites is corpus open to examination. Christianity—Stack Exchange is hermeneutics of all Christian texts and Biblical Hermeneutics studies a (very important) subset.
Finally, there is a question of site culture. Having participated on both sites, I can tell you there is a different vibe (for lack of better words) to each site. There are numerous and nearly unnoticeable differences that arise from the character traits of the people who participate. We've tried to merge seemingly-similar communities in the past and it hasn't always gone well. That's because communities differ in ways that simply can't be measured objectively.