I haven't had much of a chance to play with GitHub Desktop yet, but it can only be a good thing for the users of all Git clients - nothing like a bit of healthy competition :) However, SourceTree's focus will remain on providing the best possible experience for professional teams using Git (and Mercurial).
I've had the same experience. SourceTree has gotten better since I've started using it, but I frequently get hangs on commits and pushes on one of my machines. So much to the point that I downgraded to an older version of SourceTree.
One of the only things I miss after switching from OSX to Windows last year is Gitbox - http://www.gitboxapp.com/ - it's not free, but for what I do, it really did the trick.
This new desktop version of Github looks a lot better than its predecessor, but I need to play with it more. It does feel a lot more like Gitbox to me than SourceTree.