Should I accept the counteroffer from my current employer?

昨天和老板说了自己收到了一个 job offfer, 一个月后离职。老板问新工作吸引我的原因。我告诉他是因为新工作更fit my skills and It is more focused on reporting and analysis.... 总而言之，新工作更具挑战性。

老板先祝贺我，又肯定了我继任后对整体工作做出的贡献和改观。然后问我如果他能满足我对新工作的期望。我会不会考虑留下来。然后他又和我们院的院长去谈怎样才能留住我。他告诉我刚好四月份我们管 business administration operations 的助理院长辞职，他们先让我兼职代理，然后打广告，招人，我正式上任。They asked me to send my offer letter (I hasn't signed yet) and resume and told me I will hear more in next few days.

告诉老板前没想到他会这么强烈的挽留。但网上的建议好像一边倒 - don't accept a counteroffer.

诚请大家的建议。谢谢