It's a very interesting question, but it lacks what essentially separates Programmers (and Stack Exchange in general) from traditional discussion forums: An actual problem looking for a solution.
This, unfortunately, is not something we can overlook, it's a policy engraved in all Stack Exchange FAQs and (at least for the techonology / science sites of the network) is what keeps us all hooked, we are problem solvers by nature. You are asking us for a direct comparison of two services, without giving us any parameters that will help us decide what a good answer might be, and that's bad:
Voting, our way of measuring quality, fails.
Every feature that Github has and Bitbucket doesn't is a valid answer to your question, but you've given us no way to tell which feature (or limited set of features) would be the one you actually need, and the one that will make you switch to Github.
People will end up upvoting their favourite feature, and that not always the more helpful feature. Questions like yours tend to turn to popularity questions more often than not, and popularity isn't what the site's about.
There's a huge potential that most answers, even great ones, will be a waste of time.
As a moderator, I've had my fair share of... not so pleasent experiences on Stack Exchange. However my most unpleasent moments thus far is when I've spent about half an hour of my (limited free) time to write a thorough answer only to find out that the asker was looking for something else entirely. Don't get me wrong, the couple of times this happened, I got a ton of upvotes, but I couldn't care less about what essentially is an integer on a database somewhere.
In the case of your question this translates to an answerer writing an extensive answer about "hidden but awesome feature foo", only for you to come back and say something along the lines of "hm, nice, but bitbucket has equally awesome feature bar that better fits my workflow" or "hm, it's awesome, but it's not really something I'll ever use"1.
It must end somewhere
Lacking well defined parameters means that your question also lack limits. And although we are not looking for the One True Answer To All The Things as Stack Overflow does, we do prefer questions with a finite and somewhat limited set of answers. There's nothing in your question, as currently phrased, to stop answers appearing ad nauseum. Every time Github releases a new feature, it's a valid answer to your question2.
There are two blog posts that describe in some detail our general approach to subjective questions, Good Subjective, Bad Subjective and its followup, Real Questions Have Answers. The last sentence of the latter stands out:
real questions have answers, not items or ideas or opinions.
And for your question to become a real one, we need you to present us with a (somewhat) specific software development problem. It could be anything really, a workflow you are using but feels crude due to some Bitbucket limitation, a workflow you would like to use but can't because it's not supported, anything. But it has to be a problem, something we can feel a tiny bit proud about when (if?) we help solve. It can be trivial, or overly complex, it doesn't matter, just don't ask us to go to Github's documentation and just copy paste features from it.
However, I'm seeing there are material-if-not-overwhelming differences, e.g. Github's appealing and useful branches page versus Bitbucket's overly simple branch drop-down list.
is on the right track, but not there yet, we just need a bit more of it. But this:
This makes me wonder: what else am I missing out on? What are the lesser known Github features that folks like me using Bitbucket to save money are missing out on?
should go away completely.
I'm afraid that's all I got at this point, hope it helps.
1 Hypothetical examples, of course.
2 Certainly Bitbucket may already have the feature, but chances are they've implemented it in a slightly different way, and that, unfortunately, is all a fanboy/girl needs to write an extensive thesis on Github's superiority.