Who is to be the Imam between a person who was late for the congregation and another who prayed with the Imam, if they both wish to pray in a congregation?

It is better that you be the Imam, because you are praying an obligatory prayer while he is praying a supererogatory one. This avoids the scholarly dispute regarding the validity of a person praying an obligatory prayer behind someone praying a supererogatory one. However, if he were to lead the prayer, both your prayers would be valid according to the preponderant opinion.