I posted a similar question recently and didn't get much of a reply, and I've seen other similar posts that haven't received much of a response. Here's my two cents.
I currently work for the California state government and I'm trying to figure out the best way to transfer into the private sector. Here are three routes that might make sense for people in our situation:
1. get an MBA and network like mad
2. pursue a specific skills-based certificate or training program (and network)
3. keep the current job and try the entrepreneurial route and hope that it eventually replaces the current job
There are probably other options, but those are the three that I'm looking at right now. I think it's very dependent on each individual's situation.
If you were to decide on pursuing an MBA, I think it would be critical to choose the right school that would connect you with the right people and give you the right skills/specialization. An MBA is probably not an absolute must, but I think it's one of several routes you could take to get where you want. That's my opinion.