In Windows the Dropbox client uses python25.dll and the MS C runtime libraries (msvcp71.dll, etc). On OS X the Python code is compiled bytecode (pyc).
My guess is they are using a common library they have written then just have to use different hooks for the different platforms.
What method of development is this? It clearly isn't IronPython or PyObjC. This paradigm is so appealing to me, but my CS foo and Google foo are failing me.
Python25.dll is probably not their application code, it is a dll containing a copy of the python interpreter which can be called from within a windows application. Those pyc files are probably there in some form on windows, but they might be in an archive or obfuscated.
Python is included in OS/X, so it would be possible for them to execute those pyc file without shipping a python, but would not be surprised if they have there own python version lurking in the app bundle.
I don't know how dropbox builds there distributions, but there are several tools to bundle python apps into executable packages. Take a look at py2exe, py2app, and or cx_freeze.
Indeed they do bundle their own Python 2.5.4 interpreter found at /Applications/Dropbox.app/Contents/MacOS/python. Poking around in /Applications/Dropbox.app/Contents/Resources/lib/python2.5/lib-dynload it looks to be bundled by PyObjC.
I'm no authority on this, but it seems it is exactly as you suggest in the OP:
My guess is they are using a common library they have written then just have to use different hooks for the different platforms
Dropbox uses a combination of wxPython and PyObjC on the Mac (less wxPython in the 0.8 series). It looks like they've built a bit of a UI abstraction layer but nothing overwhelming—i.e., they're doing their cross-platform app the right way.
They include their own Python mainly because the versions of Python included on the Mac vary by OS version (and Dropbox supports back to 10.4 IIRC); also, they've customized the Python interpreter a bit to improve threading and I/O behavior.
(I do not work for Dropbox or have any inside knowledge; all I did was read their forums and examine the filenames in site-packages.zip in the Dropbox app bundle.)