Webpack 5 comes with terser-webpack-plugin out of the box, hence you can just import it and configure as you wish.

In most cases, it won't matter too much whether or not you use terser or babel-minify. That said, the benefit to using babel-minify would be tight integration with the rest of the babel ecosystem. If you are using babel outside of a bundler like webpack, or on the CLI, babel-minify can be ran at the same time as other babel transforms, and therefore requiring minimal additional config. Babel-minify would also be able to use the same cache as the rest of the babel plugins, if you have caching enabled through for example babel-loader.

Originally, babel-minify (then babili) was created because there was no uglify-js version compatible with ES6 or newer, and babel already had a parser that supported the new syntax. Since then, terser has become a good alternative, and performs faster than babel-minify while still supporting ES6 (probably because it's not tied in to babel's transform pipeline). Due to this and the reasons you listed, terser would probably be the best option to choose now.

One possible exception would be if you use experimental syntax that has not yet been standardized as part of ECMAScript, but is supported in babel's parser (possibly with a plugin). In this case, babel-minify might prove to be beneficial.

The solution turned out to be simple. Since terser-webpack-plugin includes terser, it can be used standalone.

const CopyWebpackPlugin = require("copy-webpack-plugin");
const Terser = require("terser");

And no need to add terser to the dependency list! Then we can use it explicitly whenever we want:

  plugins: {
    new CopyWebpackPlugin([
      {
        from: "./node_modules/whatwg-fetch/dist/fetch.umd.js",
        to: "./js/polyfills/whatwg-fetch.js",
        transform: content => Terser.minify(content.toString()).code,
      },
    ]),
  }

1. UglifyJsPlugin is baked into webpack2 and uses that version of uglify-js that comes with webpack you use. So you can't change it's version without changing the webpack you use (in the current master branch of webpack2 uglify-js is ^2.x.x).

2. UglifyjsWebpackPlugin uses that version of uglify-js that comes with your project (so you may install any version, stable or unstable, harmony or not).

Sources of 1 and 2 are very close.

From webpack2 documentation:

Note that webpack contains the same plugin under webpack.optimize.UglifyJsPlugin. This is a standalone version for those that want to control the version of UglifyJS.

Which one should I use in production (react app)?

In production you may try using baked in UglifyJsPlugin as long as you transpile ES6 to something this plugin accepts.

Or there is also Babili — a babel based minifier ready for ES6+ (beta).

Not sure if you're still looking for an answer to this, but now you can include the beta version of uglifyjs-webpack-plugin as a webpack plugin and it'll use uglify-es which can minify ES6 code.

npm install uglifyjs-webpack-plugin

and then in your webpack.config.js:

const Uglify = require("uglifyjs-webpack-plugin");

module.exports = {
    entry: ...,
    output: ...,
    plugins: [
        new Uglify()
    ]
};