Academically, MBA provides you with the fundamentals on how businesses are run. However, the biggest advantage of an MBA is the network that it provides you. Albeit, most schools network are in the traditional business circle.
With the start up mentor, it really depends on who the mentor is? What kind of start up it is? What your role would be? With the start up scene, the network is very important in bringing in funding and expertise. The network and expertise one has is usually limited in a specific industry. Say if you are interested in high-tech start up, but your mentor’s experience is in biotech, the mentorship may not be as helpful. Also, what role will you play in the company? If you are just a worker bee, you won’t see/participate in all the intricacies and the strategic decisions that happen. The chances are, you probably won’t unless you are an equity partner.
I would pass up MBA for the perfect start up opportunity, but would be very careful with the start up mentor. Make sure you are getting something out of it, and not being used a cheap labor.