A great deal depends upon the quality of production sound. The cleaner and more discreet the dialog the more that can be done in audio post.
Given clean dialog - and a budget and reasonable time frame - I will put in every single sound you "see" in a project. Every car pass, door open/close, footstep, telephone, computer, light switch, kiss, bed squeak, dog bark, gun shot and article of clothing will be individually created or pulled from a library by yours truly. Given clean dialog I can compose an ambience that will hopefully greatly enhance the scene.
If I have the opportunity to work with the composer the two of us can avoid stepping on each others work. As an example, if the footsteps are important to the scene I can ask the composer to avoid certain percussion instruments so that they do not conflict with the footsteps. Maybe a tense, suspenseful scene takes place in a factory; if we are collaborating I can start with droning machinery which could crossfade into suspenseful cellos and strings. This is why it is so important for both elements of the sound team, supervising sound editor and composer, to do a walk-through/talk-through together with the director. All of the audio elements will be working together when it comes time to mix so the sound design and the score mesh without a great deal of compromise.
The opposite is also true - poorly recorded production sound inhibits the ability to be subtle with the sound design and the score; you will be compromising every time you turn around. There's so much noise that it becomes a major distraction if you bring its volume down between lines of dialog. Then you have to make footsteps so loud to be heard above tho noise it becomes comic or cartoony. The subtleties of the score are lost as you now have to "carve out a hole" with EQ for the dialog to be heard clearly. Most of the time, everything else is so clean and clear that it only highlights how poorly the production sound was recorded.