You may feel bad, but if the tables were turned and the BOD felt a burning need to increase the stockholder's share by a dime, and laying you off to do so is their only way, they'll do it. Seen it happen more than I care.

Other than what you mentioned about the new opportunity, if all else was equal, I'd do it. Perhaps you could give them a couple weeks notice to allow them to get back in touch and negotiate with some of the other candidates who interviewed for your position.

No, burning bridges isn't really a good thing, but then again, there are a lot of companies out there that need your talent. I wouldn't worry about it.