The British were ultimately more successful than the Dutch and French in colonizing North America because of sheer numbers. From the start, the British came to the continent with the intent of settling it. By contrast, the Dutch and French saw the region as more of a source for resources to be sent back to Europe.
Most of the French and Dutch in North America had little intention of setting up a permanent and large colony. They had established a few cities, such as Montreal and New Amsterdam, but few ventured far beyond these. Those that did were mostly concerned with finding resources to obtain, namely furs and pelts.
The rulers back in Europe actually made it very difficult for French and Dutch settlers to obtain and manage land. They tended to be stuck on the old European model of feudal land management. In many cases, only nobility could officially hold on to land in the New World. Since most Dutch and French nobility were quite comfortable back in Europe, there was little desire to take the risk of trying to establish a new fiefdom in the relative wilderness that was North America at the time.
By contrast, the British encouraged migration to their colonies. Almost anyone could settle the land. All they had to do was establish a use for the land. The English policy of vacuum domicilium meant that any land that appeared to be underutilized could be settled by an Englishman with a serious intent to utilize it for profit.
Settlement in the English colonies was also encouraged by the rather hands-off approach of the British government. Unlike France and the Netherlands, who tried to directly control and manage their overseas holdings, British authorities were happy enough to let their colonists manage their own affairs.
This was an attractive arrangement for the many British citizens who were unhappy at home. Religious dissidents, such as the Puritans, and the impoverished came to North America in great numbers to seek a better life. Eventually, non-British colonists were allowed to settle in some of the English colonies, further bolstering the population.
In short, since there were always very few French and Dutch colonists in North America compared to British colonists, they were never able to truly compete for hegemony in the region.