Career perspective
Counter-offers: what they tell you, and what they don't
What a counter-offer says about the business making it — and about the decision you were already making.

A counter-offer is a valuation exercise carried out under time pressure by the party with the most to lose. Treated as a compliment, it is expensive. Treated as information, it is genuinely useful.
The question is not whether the money is better. It is why the conversation required a resignation.
Separate the two decisions
The reasons a senior leader started looking are rarely financial: scope, pace, a relationship, a strategy they no longer believe in. A counter-offer addresses none of those, and the ones it does address it addresses temporarily.
Write down the reasons before the conversation happens. They are much harder to recall clearly once a number is on the table.
For the employer
If a counter-offer is the right answer, the honest follow-up is uncomfortable: what else in the leadership team is priced wrongly, and who is going to test it next?
Accepting a counter-offer solves the resignation. It rarely solves the reason for it.