Even though Bitbucket and Github do utilise various underpinning technologies, I believe that this is the least intriguing distinction between them.
The two providers, for instance, have significantly different pricing models: GH charges per private repository, while BB charges each private collaborator.
Also, the ways that their issue tracking, wiki, history viewer, and collaboration capabilities operate are quite dissimilar. Github's features are a little more developed at this stage in May 2011, although Bitbucket has made significant site enhancements since being acquired by Atlassian.
(Aside: I believe that Bitbucket integration with JIRA will be extremely beneficial for both Bitbucket and Atlassian, and that is likely why they initially purchased it.)
In light of the fact that BB and GH are genuinely quite similar systems, don't merely compare them solely on git vs. hg (although git is a little crustier IMO). Examine the sites' real offerings, such as their pricing structures, issue-tracking systems, wikis, collaboration tools, etc.