Please do yourself a favor and don’t accept a counter offer from your current company, especially if you already told them you accepted the other offer.
You may be flattered you’re getting the recognition you finally deserve but trust me your employer isn’t giving you the counter offer because they think you’re a super star. They are giving you a counter offer only because you are leaving at a very bad time for the employer and keeping you is less expensive and less hassle than to find someone else.
Think about all the times you’ve asked your employer for more pay and/or responsibilities and they come up with excuses as to why. They don’t want to say that the real reason they didn’t want to move you up is because it is certainly cheaper to keep you at your current role instead of paying you more. And of course pile you with more responsibilities.
Counter offer is only to the employer’s benefit, not your benefit.
What should you do when presented with a counter offer? Don’t tell the employer, “I’ll have an answer by Monday”. You tell them, “Thank you, you’ve been very good to me but my mind has been made up”.
Give your resignation notice, leave and go seize the new job opportunity!