I think the joint degree can be a great idea. Some schools offer a concurrent program -- don't know specifically about the ones you mentioned -- where the business and law programs mutually agree to accept a limited amount of credit from the other program toward graduation requirements. Therefore shortens the time to graduation slightly.
In my opinion, one great advantage to having both degrees is learning to live on both sides of the wall. Business culture is very different from law-culture. You'll see what I mean as soon as you step foot out of law school and into the halls of the MBA program or vice versa. One is adversarial, competitive, cut-throat with a smile -- the other is more team-building, cooperative, optimizing, maximizing your benefit, etc.
IF as a law professional, you'll be serving and working directly with business people (who are not in the business of law I mean) then you will be well served by understanding THEIR language, their culture, and the context of their business goals. You'll communicate better with them. And you'll gain insights into their legal challenges that you might not otherwise have. Besides, you never know but there might come a day when you'll want to walk into their world on a more permanent basis.