You each should buy your own lunch. Or maybe you can buy each other's lunch.
If BMW hadn't decided to try to start changing their convention to even numbers for 2-doors, the car we know as the z4 would have been exactly the same as it is, but it would have been called a z3. So it is a continuation in that it is the new model year of an existing car. It is a replacement in that -- as all new models tend to do -- it replaces the outgoing z3.
The same argument applies for the E-Class coupe vs. the CLK. The E-Class coupe "replaces" the CLK, but it is really just the next model in line, i.e., a rebadged continuation.
Did the MX-5 replace the miata, or is it really a continuation?
With the 2001 model year. the 330i replaced the 328i, but nobody would argue that the 330i is not a continuation of teh 328i.
If I have to pick one side, I say that your friend wins, based on the aforementioned rebadge/continuation concept.