Can I get Notepad++-style vertical selection with arrow keys in Sublime or Atom?

Solution 1:

Sublime Text has this feature in built and it's called Column Selection functionality. It's super simple: Ctrl+Shift+/

Or, if you have a middle mouse button, just middle click and drag (in Windows and macOS).

Documentation

Solution 2:

In Atom, you can install the multi-cursor which works exactly like Notepad++.

I'm not sure about Sublime Text, but take a look at the MarkAndMove or PowerCursor packages.