You can run "webpack-dev-server", which uses your Webpack configuration to serve your scripts with its own web server.
That means (1) it can do incremental recompilation, which I can't live without since my build takes 20 seconds; and (2) it can block requests while compiling, which is way better than having a background thing (e.g. watchify) recompile your code, since it means you're never interacting with a stale (or god forbid partial) compile.
The dev server also does automatic page reloading on recompile via some injected script magic. In my case that means I often don't even need to alt-tab to see my updates, like if I'm messing around with styling.
Webpack also has a whole paradigm that expands the use cases of require() in a pretty interesting and useful way. For example, you can tell it that require("../../icons/lolcat.png") should resolve to "static/lolcat.[8 chars of base64 SHA-256].png" and also do the appropriate file copying. Or you might want require("./stuff.csv") to resolve to a parsed JSON table, or any such transformation. There are a bunch of plugins for common uses. It's common to use require() even to load your CSS, because then Webpack can handle running it through your auto-prefixer or whatever.
It might seem kind of bloated, and I love Browserify for its simplicity, but I've come around to really like Webpack now that I've spent the proverbial 4 hours.