Another, it depends situation
If the job offer is better, then why are you even negotiating with your current boss?
Be aware of what the compensation rates are in your area for your job and responsibilities. If you're below the average compensation, then mention that first, not that you've received a better offer. If you're not at the capped rate for your company, use that first, not the offer. Or use a redefinition of your position as not matching the job description and salary.
I'm a 20 percenter myself. I'm not walking until I get a total package that's a 20% or more improvement over what I currently have.