Having been in such positions multiple times when evaluating job opportunities, I found it to be fairly simple - please remember it is a business transaction and take as much emotional experiences out of it
you, and only you, already know what you want to work for in terms of compensation and what is your lower bound. Give yourself a deep thought of what those numbers in, work towards an offer (without an offer there is _nothing_ to talk about), and then negotiate.
If they ask on why , you can mention comparative benefits. Beyond it, your market value is what you are willing to work for and what others are willing to pay for your skills and experience.
if they can give you what you want -> take it
if they cant/wouldn't -> walk away.
as prospective job searcher, I don't really care of why company does not want to comp you the way you want to be comped (owner dealing with divorce, the moons of Saturn aligning, etc). Who cares?
as hiring manager, similarly I don't care about any sob stories (your dog needs a surgery and that makes you deserve higher pay, your agreement with ex wife , your children braces, your gambling debts, etc). Who cares? This is what I can pay, and the range I can use, we either meet or don't meet.
it is a business transaction , treat it as such. especially if you are going for at will employment..