Well, being content and happy with your current state is pretty much not compatible with high ambition and continually striving to achieve more, it's a tradeoff.
As in the old quote - "The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man."
Contentedness and happiness are very different things. The former comes from the inside. It is a sense of satisfaction and peace. The latter comes from the outside. It's a sense of elation and joy.
The reason your post presents a false dichotomy is that it is possible to be both content and happy. In fact, people should strive for a balance of both. Being content should not get in the way of attaining happiness, or vice versa.
As in the old quote - "The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man."