Well, I can say that you and your buddy are both correct to different degrees.
If you already have the code for a game the best option is to use as much as you can from it and ship it... it makes business sense to do so. But in reality you can't use the 100% as it is, even when porting it to a new platfrom requires some level of adaptation to support the new platform... some times you can think of a remake as a simple porting to a new platform... other times you add some new functionality that wasn't present before (like adding achivements to PS1 games)... and if the original game has some decades behind it its very possible that the hardware architecture and technology has evolved in that time that most of the original code simply won't work on modern platforms (games are heavily optimized with low level tricks to take as much advantage of the hardware as it can)..
So, the degree to which you would decide to use more or less of the original code would depend on how different is the platform you're targeting at, how much technology has evolved, and how much new functionality you want to ship it with.
Just consider that porting a game from one generation (say XBox360) to the next (XBoxOne) needs to be changed in so many little places that it's not worthy for Microsoft to release all of them again because of the work it implies.
In the specific case of Link's Awakening, you're talking about a 2D game that was originally made for a monochrome platform from 1989, under a 8-bit architecture with limited resources (8kB of RAM).. things have certainly evolved now... and changing it into a 64-bit full 3D game, and with a few adpatations on the gameplay mechanics to make it feel more modern.... I'd say in this specific scenario there's no way the original code would be of any use.... i't would be way simplier to just make the game from scratch again.
On the other hand, the remake of FFVII for PS4 (not the remaster they're doing right now) probably that takes at least around 70% of the code on the original game released on PC on 1998.
My 2Cents
"lots of shoulddas, coulddas, woulddas in the air, thinking about things they shouldda couldda wouldda donne, however all those shoulddas coulddas woulddas ran away when they saw the little did to come"
