While I use WebStorm for larger projects such as building a website for someone or collaborating on projects at school.
Sublime Text, to me, is still just a text editor (a really good one at that), while WebStorm is a fully-fledged IDE.
I prefer SublimeText as a TextEditor. I've been trying to use Atom, but haven't made the complete switch.
I've been playing with WebStorm because I think JetBrains products are #KickAss.
I would recommend to using the best tool for the job/task you're working on. If you're doing .NET Development, then Visual Studio would be your tool of choice.
If you're doing web development for MEAN or LAMP or anything else, you're probably use a combination of SublimeText/Atom and something like WebStorm.
I suggest trying to use as many tools as you can and see which ones work best for you and your workflow. It's always a good thing to know how to use more than one tool.
About 2 or 3 years ago I was introduced to Rubymine (also by Jetbrains), and from there have fallen in love with their products. I have personal licenses for Rubymine, PHPStorm (of which WebStorm is a subset) and use IntelliJ and PyCharm regularly. Their products 'just work' (Linux, OS X and Windows), and the similarities/consistencies between the different editors make subsequent learning curves much less steep. I've been using the CLion EAP a bit, and will likely be paying for a license when it's released (simply because it works that well out of the box).
That said, I will still use vi to do small text edits or JSON file changes etc if I don't need the entire IDE. So I think it is a pick the best tool at the time. I also will use notepad++ if in Windows the same way I would vi on my Mac or a server.
I personally haven't used SublimeText but I know a lot of people swear by it for its flexibility.
I'd use SublimeText otherwhise :)
For everything else (mainly Go/Python these days), I use vim.
WebStorm is great if you need to manage a project as it grows, but if you just want to bang out 200 lines in a few hours, SublimeText is much more lightweight.
I choose the tool depending on the size of the code base.