In comparing these two as to which has ultimately proved stronger as the base for popular rule and why, one can discern that the French revolutionary tradition has accomplished this for two reasons. The first reason being due to the fact of it being more recent in historical context. Such an important event having occurred less than 300 years ago has more relevance in the minds of many political thinkers in our modern era than a similar event which occurred nearly 800 years ago. Mankind tends to believe that his ideas improve over time and thus the later the idea, the better the idea it is.
The second reason for the French tradition being the base for most forms of popular rule today is due to it truly identifying and involving the three classes of the populace the aristocracy, middle-class, and poor, back then as it does today, in the political and economic process of society. While both traditions sought to limit the power of the monarch from being absolute over its subjects, it was the French revolution which gave a strong voice to those neither rich nor poor.
The English tradition on the other hand, primarily involved the nobility and the monarch, much like a dispute being settled today between the millionaires on one side and the billionaires on the other. Today, like in the late 18th century during the time of the French revolution, in most advanced and developing democratic societies, the vast majority of the citizenry fall in the middle.
Thus, it is their political interests and perspectives which influence political discussion and change, just as it did nearly 300 years ago.