Q: When I gave notice at my current organization, they made me a counter offer. Should I accept it or move on?
A: Before answering, you have to ask yourself why it took an offer from another company to get an offer worth keeping from your current employers. Counter offers always make me nervous. Did you ask for raise and show them you were worth it before job hunting? If so, that means the company failed to accept your worth until you threatened to leave. That isn’t a very good company / manager. If you didn’t give them the opportunity, then you failed.
The loyalty has been weakened on both ends of the spectrum now and many companies who make counter offers do it only until a replacement can be found for your position. Obviously, that is not always the case - there are plenty of cases of great outcomes from accepting counter offers - but I believe those are the exception that proves the rule. Consider counter offers from every angle and with eyes wide open.