In my opinion the only way you accept a counter offer is if there is an agreed upon severance package that is essentially unconditional presented to you in writing as part of the counter. If you stay right now, they see you as a flight risk. If you stay but they need to pay you 3, 4, 6 months pay in a lump sum to lay you off or fire you, they know that you have stability due to that, so shouldn't be a flight risk, and you know that even if they lay you off, you're good financially.

IMO without a pre-agreed upon severance deal in writing, that does not have an expiration, I wouldn't accept a counter offer. If they are willing to offer me that, I go to teh new company and present them with an offer of X% above net compensation that my current employer is now offering me to stay plus a pre-agreed upon severance deal there too. If they balk, I stay at my current spot.

Having that safety blanket would be incredible and I think it's the only way to make staying worthwhile. I would be too stressed out thinking I'm perceived as a flight risk otherwise.