Why not both?
"You can have a chocolate or ice cream. Which do you want?"
I posed this question to my son. To nobody's surprise, he rejected the choice and answered "Both". Repeating that he should only choose one of the options were in vain. What he knew very well was that the choice was artificially imposed by me and there was way he was going to fall into the trap of choosing one.
These kind of choices are known as false choices. Most of the time, we are faced with such choices which for some reason we believe we can only have one or the other. In the story of the ninety nine heads, we saw that we often make assumptions that we take granted for true. It's the same here, and innovation occurs when we reject the false choice and think about "Why can't we have both?"
Here is an example: Software developers are fond of telling management that quality takes time. We can either take the time required for ensuring quality, or we can cut corners and deliver fast. You can choose, which one do you want?
This is the perfect false choice. You can have both. Most software companies that have high quality also have a tendency to release fast. This is because processes are highly reliabe, lots of things are automated, and the entire release process happens multiple times a day. Once you see these systems in action it becomes obvious that high quality and fast releases are positively correlated. Yet, this concept was unimaginable twenty years ago.
So the next time you are in a dilemma of "this or that?" its worth asking the question: "Why not both?"