if money is what you are moving for, then definitely take the counter offer since it pays more ... otherwise, if you are moving for a better work environment, better growth or do not like your present company, it is better to move on.
I know a guy who worked for a small sized company which was headed for a disaster and this guy was a VP .... He got an offer from another small sized company but his current boss then talked him out of leaving .... by offering him a raise and a promise that things will get better. Anyway, the company continued to go south and went into bankruptcy some 6 months later.
It is situational ... there cannot be a standard answer.
