re: Etiquette for turning down job after accepting?

I would not stay with your current job nor would I let the new employer know about the counteroffer. Your current job now knows that you are looking to leave (even if you accept their counter) and they will be looking to replace you as cheaply as possible. If you tell the new job about the counter offer, they might think you were just using them as a bargaining chip.

It really depends on the culture of these companies. Will either of them be offended by your using them as a bargaining chip? A lot of companies are totally fine with that and actually expect it. But some companies will get super p*ssed and blackball you.