Nowadays not a lot more, but when it came out it was a revelation.
The key thing to note is that replicating webpack's abilities in browserify takes about the same or more amount of config and boilerplate.
The main difference was that WebPack bundled it all together so it was all ready out of the box.
More generally, browserify seemed very Node-focused in attitude and webpack made a lot of design choices particularly for the web. Things like having uglify built in, ability to not just bundle javascript but also other assets (like pictures and css). I bet all these things were possible with browserify, given the right transform, but I liked that with webpack it was the norm. It seemed designed for the problem I had: coding a web app. Browserify seemed designed for "I have this huge node program that i want to port to the browser with a little effort possible".