Note (added 9/29/2015) this post is a bit obsolete: in Spyder, be sure to go to Preferences-Editor-Code Introspection/Analysis and turn on Automatic code completion.
After just a day with Pycharm (and a few weeks with Spyder), it is clear that for PySide coding, Pycharm wins. However, for scientific computing, especially for those who prefer a quick-responding Matlab-like IDE, Spyder definitely deserves drive space.
Spyder IDE for a few months now. Strangely, while tab completion works in its Python shell, it is not always seamless in the editor window (as discussed at http://code.google.com/p/spyderlib/issues/detail?id=1254).
Note added: to minimize this issue, be sure to go to Preferences-Editor-Code Introspection/Analysis and turn on Automatic code completion. This has made PySide tab completion work in my editor, and now I am back to using Spyder for PySide coding, and this makes this post somewhat obsolete frankly!
I've never placed much stock in IDEs, but as I watched some excellent PySide tutorials (found at http://www.yasinuludag.com/blog/?p=98), it seemed Yasin Uludag was able to type PySide code at mach speeds partly because of the IDE he was using (and also partly because he is a badass PySide ninja).
To see for myself, I installed the free version of Pycharm yesterday.
First good thing I noticed: no install hell. Installation was easy on Windows 7. It automatically saw my Anaconda distribution of Python, and automatically used iPython for command line work.
Upon firing it up, the first thing I noticed was that Pycharm was really slow to load, and also very sluggish in response to basic commands (even entering text or surfing the menu system). Thankfully, it grew more responsive over time (or perhaps my temporal expectations adapted to its intrinsic pace).
Despite the slow start, after about five minutes of exploring (with the help of the Getting Started page), I started to appreciate the crazy horsepower under my fingertips.
I haven't really touched the surface of Pycharm. I still feel like a 16 year-old who just learned how to drive stick, and was given the keys to a Ferrari. A bit in over my head, but excited nonetheless. Pycharm seems seamlessly integrated with version control, unit testing frameworks, has all sorts of refactoring functionality built in, among other things I have not yet explored and have never used before. I won't go over all the details, as I am just starting to learn them myself, so if interested I'd ask Google.