You don't need scientific research to know that a good extensible, programmable editor that can become an extension of your mind and hands is going to make you more productive than Notepad. It's like playing a musical instrument. The finger movements and thought processes move into the background over time as you master them with proper practice and you start operating at a higher level. A world-class musician isn't thinking about which notes to play when and where to put their fingers but rather how to put more emotion into a performance.
Similarly, a top flight programmer who has mastered emacs or vim or Sublime Text won't be operating at a conscious level but will be controlling the environment in front of them at a far higher level, especially if the conceptual model of the text buffer is the same no matter what they're doing with it.
An extreme comparison would be to sit two people of the same ability down in front of the Linux kernel source tree, one armed with emacs, cscope, syntax highlighting, org-mode and cc-mode and the other with nano and see who is faster at some non-trivial task.
You don't need scientific research to know that a good extensible, programmable editor that can become an extension of your mind and hands is going to make you more productive than Notepad.
Sure you don't. You can feel the difference. The problem occurs when people treat their editors as an extension of themselves and can't tell the difference between "not liking you" and "not liking your editor", eventually getting defensive. That's a "cognitive level" I don't want to get myself into.
There will always be flamewars and defensiveness about technology choices. Some people are insecure, some aren't. Not everyone becomes a dick just because they've mastered an editor. My best friend for many years used vim while I used emacs and we used to constantly rib each other about our choices. But we still worked very well together. Maybe you need to work where people don't care what you use to get stuff done as long as it gets done?
It doesn't have to be measured to 7 significant digits in a scientific way. But if you spent a week trying out various editors every now and then for the kind of work you do, you should at least be able to make a more informed choice about which editor to use. Or you may discover functionality in another and see if you can get it in your current favourite.
I've interviewed people who were exposed to Nano at school, and have never tried out any other editor. They are missing out on productivity improvements available in many other editors. More middling of the scale I've also interviewed someone who used Eclipse as their first editor and has proceeded to use it ever since despite not working on Java projects any more. That isn't bad per se, but I rank someone higher if they at least try out others every now and then.
How do these people know it makes a difference? Do they measure their productivity? Is there any scientific research on this?