In my experience, it's the players that decide how the game is played, not the system. When discussing the various editions of D&D, at least.
I have found no difference between how my group approaches 4E to how they approach 3E. Other than some of the words used to describe things, the game plays the same. Conversely, I have played AD&D is many different ways in various campaigns (combat-heavy, pure exploration/investigation, political intrigue), so saying that the system determines how the game is played seems incorrect to me.
In my experience system effects gameplay a lot. Everything from how long combat takes to the dynamics between characters at the table. Whether you are able to play an epic hero or gritty spy; system definitely has an impact. You can always work around the system but the system itself is the toolbox you draw from. I would say 2E, 3E and 4E all play very differently in my experience.
You're both right. And the premise (or promise, or promised premise) of 5e is that due to a streamlined and balanced core, with optional add-on modules, you can both play in that same sandbox. Perhaps there is even a way the epic hero and gritty spy can play at the same table?