Companies present counter offers to keep their intellectual property from walking out the door. It is about them not you. Just ‘google’ the phrase counter offers and you will come across plenty of websites all telling you not to accept a counter offer. Your loyalty will always be in question and if you have already had that all important conversation with your Manager concerning your unhappiness question why you are only being listened to and getting improved conditions after your resignation. Only you can make the decision whether to stay or go. Don't let anyone pressurise you, ask for a few days away from the office to make your decision. If you decide to stay and things do not work out you will just have to start the process of your job hunt again!
Such a difference in approach
a true professional well organised with a willingness to help