Built by the company "JetBrains" who are pretty well known for their "IntelliJ IDEA" product that works with Java and the JVM in all its forms.
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Pro Sophisticated autocompletion
PyCharm includes sophisticated heuristics for determining what each variable type is and providing autocompletion suggestions for them.
Pro Excellent refactoring support
There are many refactoring options including renaming and changing signature across entire projects. It also includes the an ability to preview changes before committing and exclude anything unwanted.
Pro Community edition
There's a community edition that's free to use. You can also get a 30-day trial of the Professional edition.
Pro Version control integration
PyCharm has CVS, Git, Subversion and Mercurial integration.
Pro Catches run-time information when running the code
PyCharm can leverage run-time information when running your application with the built-in debugger to figure out what types can possibly be passed to which functions, etc.
Pro Built-in Django support
Pycharm has excellent django support, from templating to management commands, it has it all.
Pro Sophisticated static analysis tools
Pro Supports installing 3rd party libraries
No need to go to the command line to download a new package, PyCharm has an easy system to browse, download, and update 3rd party packeges.
Pro Automatically figures put what test to run based on the method the cursor rests at a given time
PyCharm, based on what method or class the cursor rests, can figure out what tests to run and perform them with a keyboard shortcut or two, without breaking up the flow and need to switch to a command line interface.
Pro Free student access for Professional Edition
With a valid .edu address students can register to use the Professional edition and enjoy all the perks of the full paid version for free.
Though it should be mentioned that the with the free student acess you cannot use PyCharm for any commercial purposes, even accepting donations for an open source project.
Pro Vim mode for people used to Vim commands
IdeaVim supports motion keys, insert mode commands, marks, registers, visual mode commands, vim regexps, key mapping, macros, digraphs, some ex and :set commands. You can find a full comparison in the IdeaVim reference manual.
Pro Remote debugging over ssh coupled with automatic deployment creates a streamlined workflow
The professional version allows remote debugging over ssh, which together with automatic deployment creates a streamlined workflow.
Con Does not support inline plots
Spyder supports the inline plot function of matplotlib, not the case for PyCharm.
Con Some relatively basic functionality requires paid license
Con Odd Autosave "feature", can't be disabled fully
PyCharm automatically saves your files for you, always, without telling you. You can't disable this. There's a way to indicate if a file has been modified via an indicator in the tab (not enabled by default - why?). If you exit it won't ask you if you want to save the modified file. Totally unintuitive and contrary to all other established workflows. It's ok to try something new, but give users the option to have the "normal" behavior of any other IDE/editor out there. Can be a deal breaker for those that need to know/have control over when they save their files. (PyCharm offers a history to undo the automatic save, but why force a user to undo something with extra steps that shouldn't have happened in the first place?)
Support for runnink flake8 directly
Con Can not be integrated with external linters, like Pylint, Flake8, etc.
Sublime Text has SublimeLinter, Vim has Syntastic, PyCharm has nothing.