What does phpStorm give you that sublime doesn't? Refactoring tools are nice and deployments configuration are nice but the tradeoff just loading the app in terms of speed can feel like minutes.
I'm not a Sublime expert but: great Git integration, database management, Xdebug handling, all those extensions (the Symfony extension is basically magic, and that is just scratching the surface), I could go on.
And yes I sometimes wish it would be faster, but not enough to use something else with a quarter of the functionalities.