Using Node.js require vs. ES6 import/export

Are there any performance benefits to using one over the other?

Keep in mind that there is no JavaScript engine yet that natively supports ES6 modules. You said yourself that you are using Babel. Babel converts import and export declaration to CommonJS (require/module.exports) by default anyway. So even if you use ES6 module syntax, you will be using CommonJS under the hood if you run the code in Node.

There are technical difference between CommonJS and ES6 modules, e.g. CommonJS allows you to load modules dynamically. ES6 doesn't allow this, but there is an API in development for that.

Since ES6 modules are part of the standard, I would use them.