Personally I use both, continuously switching between the two. I play around in ipython/pylab until I've gotten all the algorithms and details worked out, and then use Pycharm to add that code to the larger library or application which those algorithms will be a part of.
If you do a lot of development in the REPL (i.e. exploration), then that is where iPython (in a notebook, or a shell) really is nice. If you don't, then you may not see the benefit.
I primarily program with python for shell scripting/text processing, or data analysis/simulation with numpy/scipy/pandas.
I do a lot of exploration, I rarely ever type anything directly in the REPL/interpreter - I write all my code in scripts and send them to the REPL with emacs keystrokes. Afterwards, I'm left with a script that contains my analysis/processing method. (never had a local web server running except when playing with emacs ipython notebook).
Am I possibly missing a way to do it better?
I find ipython with its magic commands and ability to directly call shell commands more handy than the standard REPL for interactive shell type scripting.
Other than that, not really. Inline graphs are nice if you like that sort of thing, and some of the magic commands are occasionally useful. But beyond that I don't think you'll gain much if you have a approach that works for you.
I also gather that ipython's parallel processing tools are pretty powerful, but I've never really played with them.