What sucks about when your current job gives you a counter-offer is that they may be totally pissed if you don't take it. My first job out of college wouldn't accept my resignation, made me a counter-offer, and kept asking my for reasons to explain why I was leaving. They wouldn't accept any of my reasons and kept asking for more and me being a stupid guy going through his first resignation kept telling them reasons. Needless to say I would never be able to get a good recommendation from that company...even though their persistance in trying to keep me on showed how much they liked me.
Anyway...when resigning, the less said the better. Don't tell how much the new place is offering. Don't give your reasons for leaving.