Which is better? Simple or complicated? Can they help one another? Regarding this matter, Seth Godin provides this gem:
your goals and your strategy must be simple. You must have passion and certainty in order to make a difference as a leader. Your tactics, on the other hand, should be layered, multi-dimensional and reflect the patience of someone who cares about reaching a goal.
My take: if the goal is to explain it to someone else, make it simple. When thinking operations, don't worry about making it more complex. If you achieve this sensitive balance, you won't have to worry about over-complicating a single thing.