Here's the first hand word on BNI, as my husband is currently the president of his section. . .
As an independent electrician, this has been an extremely valuable marketing tool for him and is actually the only marketing he does. His business has been built entirely on word of mouth through this group. However, I am not sure there would be a huge value for an engineer being in one of these groups, depending on your specialty. He's had architects and general contractors in his group, but no engineers.
A typical membership might include a remodeler, insurance salesman, chiropractor, marketing firm, uniform rep, audio/visual installer, landscape architect, lawyer, realtor, and so on. His group tends to have people who own their businesses or work for small businesss more than people representing a major company, i.e. Joe the insurance guy, not Bob with AAA.
These are groups of about 30 professionals, and the sole purpose is to generate referrals to other members. Each time you attend a meeting, you should have a referral for at least one other member. You should have a big enough network already that you will have friends who might be moving and need a realtor, or maybe your neighbor is painting her house, etc. That's why I don't know how valuable this would be for an engineer. How many times does someone have an opportunity to refer an engineer to an acquaintance?
As for cost, you can visit as a guest for free maybe once or twice, depending on your section's rules. After that you can apply, and they can accept or reject your app. It's about $300-400/year, but if you serve as an officer (which is typically required at some point), you'll get a reduced rate for the next six months.
Another important note is that you're expected to be there every week or send a sub. The sub can be an employee or your grandma (if grandma happens to have a service business to promote), but your only allowed 2 absences without a sub or you can be asked to leave the group.
Hope that explains BNI a little more for you.