Pros
Traditionally MITRE has been a very stable job where you could work on hard problems for the government outside of the bounds of federal employment. The pay is better than working in government, and the people are highly educated and generally hard working. Also, as a not-for-profit, you can focus on finding the right solutions to government problems without worrying so much about selling your company's products or services.
Cons
As a consulting firm, the same pressures of getting work do apply, and MITRE has traditionally not done as good of a job in working with outside entities or partnering with top organizations, although there is management pressure to do so. In a company of 9000 people, though, it's easy to just think about your skills and your team's potential, and not think about what could be done by partnering with the outside world. That said, if you want to grow at MITRE, you really do have to spend time on work that is not billable to customers, such as writing proposals.