In Node.js, there's no inverse of Buffer.toString; instead, you pass the base64 data directly to the buffer constructor, along with a flag indicating that the data is base64 encoded.
If you want to run the example as it appears here, you'll need the buffertools module installed, in order to get the Buffer.compare method. To get that, run npm on a command prompt:
npm install buffertools
If all you're going to do is use the Buffer constructor of Node.js to decode base64 data, you don't need to do this.
Here, we'll take our original buffer and compare it to another one initialized with the original base64 for the first message:
require('buffertools').extend();
var buffer = new Buffer('Hello world');
var string = buffer.toString('base64');
console.log(string);
var another = new Buffer('SGVsbG8gd29ybGQ=', 'base64');
console.log(b.compare(another) == 0);