How did the colonial strategies of the Spanish differ from the approaches of the Dutch, French and English?
All of these nations had at least three things in common during colonization: Christian religion, superior technology, and an economic stimulus, with economics being the most universal factor. Virtually every nation and person who engaged in colonizing activities did so for money, in one way or another. The entire impetus for exploration was trade, specifically in spices, which were predominately located in the East. Explorations to the West were generally conceived of as a means of circumventing both the hostile Ottoman-controlled lands in central Asia, and the Venetian, Portuguese and Dutch control over ocean trade routes to the East.
The Dutch were distinctly economic in their interests; they had little concern for establishing forts, homesteads, religious centers or improving the quality of life in their colonies, with South Africa being the exception. One famous example of this was the exchange of New Amsterdam (modern New York) for an English claim over one of the spice islands, allowing the Dutch a monopoly in nutmeg.
The French and English were generally late-comers to international colonization; their navies were relatively ill-equipped compared to other nations and stagnated significantly until the Battle of Trafalgar established Britain as the dominant naval power several centuries later (the perception of colonies and empires as a British-dominated practice should be largely confined to the 19th century). France's motivations in the Americas were, initially, largely trade-oriented, particularly in North America. Like the Dutch, the French tended not to create cultural centers or encourage large populations, which made enforcement of their claims difficult. Most of these territories were lost in subsequent wars or sold off, as in the case of the Louisiana purchase, when the effort to maintain them appeared to be more than the territory was worth. The key difference with England was the encouragement of an agricultural and cultural establishment.
The Spanish were unique in that they were the most religiously-motivated of these nations. This is likely to be due in part to the intense Christian fanaticism fostered by the Reconquista and the Inquisition, as well as the encounters between Spanish explorers and the most "civilized" cultures in the Americas, which practiced cannibalism, human sacrifice and other "satanic" beliefs which led some of the Spanish to believe that the Native Americans truly did worship Satan. The Spanish were able to afford these sort of behaviors early in the colonial period because the only other real contender for colonization practices was Portugal; indeed the famous Treaty of Tordesillas divided the entire world between Spain and Portugal, although the other European nations ignored it. Spanish influence was not strong in North America because these regions were not perceived to have as much economic worth, nor were they well-known for the "cities of gold" myths.