One big set of features missing are the configuration options available in PyCharm. For example being able to configure Vagrant in PyCharm provides its own UI in the IDE settings. I have created a screenshot showing all the various PyCharm setting views compared to IntelliJ with the Python Plugin installed:
You can actually get some of the Vagrant features with a separate Vagrant plugin in IntelliJ, but PyCharm lets you set up the Python interpreter with Vagrant via a really nice UI.