Not working in the industry, but probably the latter.

Designers can come up with nice ideas, but often it needs to be play-tested before you can decide if it is good for the game. If it doesn't, stuff needs to be modified.

Also, I would expect programmers to have little to say about the game design. It's not your job to invent or design a game mechanic, your job is to realize their design in a piece of computer code.

In the latter however, I would expect much more freedom and creativity for programmers. Designers don't understand code, they likely don't care how you code things, just get it working as they want it. Obviously, the latter isn't necessarily easy to achieve with a dumb collection of silicon, some metal, and a few wires, commonly known as “computer”.

From what I learned in past 8 years in the industry is that programmers are the most needed but most unvalued resource on the market. In my first job, the game design was made entirely from a game designer that always guided to her design document when there were questions.

On the second project we had a more open discussed game design but the company owner took action and changed the purpose of the game in mid of development and set focus on a story mode that was never intended in the approved design doc. No big suprise that the game failed to perform well because of that.

And that was similar all the way for different employers and projects all over the time. Now in a more “professional” environment, the game design is entirely in hand of the design team. Programmers are executing material, no more, no less without any influence on the game design. It might be kind of a common process as AAA developer that there are teams for everything. Features are planned by the leads and must comply into the game design that is created from the design team and needs to be approved by the studio-wide creative director.

Prototyping a game or game feature was already made by the designer; we used Unity so a programmer just had to provide editor extensions and features so that the designer could test gameplay elements, mostly using a drag&drop editor maintained by a pogrammer. The only exchange I ever experienced was for the designer to request coding work to be done for him to be ale to test new gameplay items.

TL;DR: From my experience, if you want to make a fun game that everybody in the team is enjoying to develop then you probably best fit into a larger indy studio or mid sized regular game studio while if you just want to do headless work, AAA game studios are your place to be