There's quite a bit of variety on "the business side", FWIW. Getting an MBA does not necessarily get one increased access to it, depending on what you want to do and where you want to do it.
Dave McClure had a really good discussion once on starting a startup as the new MBA: far more interesting to hear you talk about how you sold $200k of sales than hear about how you read about someone doing the same. This also gives you a lot of opportunities to directly apply engineering skills in the service of your business goals. Those opportunities exist (in quantity!) in real life, but may not in any given MBA program.
And for the management side, growing an engineering team from 1 to N will teach you more about people and (early-stage) organizational dynamics than any number of case studies. However, learning by doing -- and potentially failing -- doesn't appeal to everyone, and you can certainly balance the "on the job" learning with book-learning too.
I did an executive MBA, and plan to move into people management at some point. I enjoy it and I love the feeling of empowering a team to be excellent. At the same time I feel that you need a solid base as a respected individual contributor, especially if you are leading the team technically rather than playing bug-assignment Tetris -- which is what I'm focusing on for now. Management can seem like a dirty word in engineering, but some of us like doing it.
Dave McClure had a really good discussion once on starting a startup as the new MBA: far more interesting to hear you talk about how you sold $200k of sales than hear about how you read about someone doing the same. This also gives you a lot of opportunities to directly apply engineering skills in the service of your business goals. Those opportunities exist (in quantity!) in real life, but may not in any given MBA program.