How to debug .app that only successfully launches from Terminal?
You could start by tracing the executable:

% sudo dtruss /Applications/Dropbox.app/Contents/MacOS/Dropbox


It may be loading the wrong python, etc.  Sometimes a trace will give you a clue as to where your app is crashing, esp. if you only have an executable.

You can also look at how the executable was linked, maybe it's finding the wrong version of a library (ldd on linux, otool on osx):

% otool -TVLrH /Applications/Dropbox.app/Contents/MacOS/Dropbox