Both products are made by Sizzix. The Vagabond has an electric motor, while the regular Big Shot doesn't. Because it's motorized, the Vagabond cuts chipboard, Grungeboard and other thicker items easily, although the Big Shot will cut these items as well.
The Vagabond folds up when not in use, making it easier to store and is in a decorative suitcase shape when closed. The Vagabond is the more expensive of the two.
You can find several discussions about the differences online. Here
is a great thread in our forum about the Vagabond and how it compares to the Big Shot and Big Shot Pro. I hope this helps.