GitHub vs. BitBucket
Status Quo
For MoinMoin development, we use some self-hosted mercurial repositories at http://hg.moinmo.in/ plus a mirror on https://bitbucket.org/thomaswaldmann/moin-2.0/ for easier collaboration.
We use mercurial because we like python software and also because it was (is?) easier to run it on windows. As a python project, we support multiple platforms, including windows.
We use bitbucket, because it is the most popular public mercurial hosting.
GitHub vs. BitBucket
github has recently become way more popular than bitbucket, is more responsive and has a nicer feature set / better integration.
otoh, bitbucket has not developped that much. the issue tracker lacks essential features like tags. it is slower. and (maybe most important): it is less popular amongst developers.
But: as the name says, it is based on git and they do not support mercurial.
git vs. hg
With github, the most direct way to use it is of course by using git.
If one wants to continue using mercurial locally, there is hg-git. I don't have personal experience with that though.
Developer Opinions
I somehow would like to move from bitbucket to github. OTOH, I like mercurial and maybe would try to continue using it. I have a rather simple workflow though, so I could also switch to using git locally. Not sure about how to proceed with the self-hosted repositories, guess they would need to get converted to git if we move to github. Alternatively we could stop self-hosting it publically and maybe just have a current backup from github. -- ThomasWaldmann 2015-02-14 19:48:32
I find the github website confusing. If one goes to https://github.com/mirror/moin-2.0 (or any other project), there is a table of folders/filenames, descriptions and dates. The contents of the table rows seem to be chosen at random and sorted in a random order.
The github web pages tend to have lots of light gray text that would indicate a disabled function on most other web sites, but at github some are hyperlinks, some not.
The github issue tracker seems inferior compared to the one on Bitbucket. The right side menu is awkward when viewing the issues page in a narrow window. I find the colored labels distracting. -- RogerHaase 2015-02-16 16:16:58
@ roger: that table is just the branch contents, all dirs/files in their current state (the msg it shows for each file is just from the last commit when that file was touched). It is sorted alphabetically like file managers would also do. Mercurial (hgweb) has a similar view (but it is not default, see "files" link).
gray text: maybe just a matter of taste. While contrast is lower, it doesn't look as harsh because contrast is lower. 
issue tracker: I practically used it in some projects (e.g. there: https://github.com/nsupdate-info/nsupdate.info/issues ). While it is a bit simplistic (I miss the basic scalar values, but the one github has is crap also), it is quite usable and the labels are very useful. E.g. we are often asked for easy beginners tasks, on github you can just have a label for that and it even will stand out on the complete list due to its colour (one can also click on a label to only show issues with that label). One also can define milestones, which are basically subsets of all issues that should be fixed for reaching that specific milestone, which is very useful for release planning (see examples in nsupdate project).
Window seems to need 1200px width, yes. I didn't notice that yet as I usually have more than that.
-- ThomasWaldmann 2015-02-17 13:26:58
The current situation is a mess, BitBucket got bascially killed by atlasian, and github does not intend to support mercurial.
That leaves a wanting situation, im currently hopeing for kallithea enhancements for collaboration, and would like to defer the topic until aftter moin 2.0
Something I experienced today was editing the commit message (which was pushed) I had incorrectly typed before.I was missing git at that moment.
Another benefit of moving to github would be gitter https://gitter.im/ (Alternative to IRC). It has many awesome features and is directly integrated with github. [Shows recent commits , merges.. , sends email notifications.. etc ].
Other benefits :
1. Unlimited chat history
2. IRC gateway available
3. Easy to use , integrated with github.
Billing : $0 https://billing.gitter.im
Angular , Rails , Sympy are already using it.
Example: https://gitter.im/rails
My own opinion
Github is an hosting platform for open-source project but github is not open-source however github is very popular. My opinion is to maintain github miror only like miror. Don't use gitter. take on an irc-server or better an xmpp -server. Host your project on a free & open source platform. Kalithea is a very good choice If your choice is to keep only git there is gitlab or gog. If the project of your choice lack a good bugtracker, maybe you can run a only bugtracker project like tracks or bugzilla
- --vicking