Books have been written about this subject. While both European powers came to the New World with the distinct intent of subjugating it for their own use, there are some significant differences evident in both the Spanish and English colonization of the Americas.
One particular difference is the time period of each. Much of Spanish colonization of Mexico and South America takes place in the late 1400s and early 1500s. No other nation had made such a foray before. Thus, the Spanish had no frame of reference to guide them. How they acted was a direct reflection of a lack of predecessor. This is fundamentally different from the English colonization of North America, which takes place in the 1600s. The difference in time allowed the English to absorb lessons from the Spanish failures, thereby allowing for a longer and more profitable hold over North America than the Spanish had over Mexico and South America.
Another difference is administrative. The Spanish conquering of Mexico and South America and Mexico was done under the Royal Crown of Spain. Spanish monarchy was the initiating agent in all Spanish exploration. This meant that Spanish royalty was the funding source for all exploration and fed the absolutist notion of the Spanish state. However, as Spanish government found itself immersed in other domestic realities like war and conflict, it could no longer give the required amount of focus to exploration. This was not the case in England, where companies and charters dictated exploration. Given how organizations were able to fund organizations, this meant that both quantity and sustainability of these ventures were expanded over what the Spanish could do. More growth of these companies, as exploration proved fruitful, could enable greater and more varied expeditions to present themselves. This was not the case in Spain, which had limited upside for growth and potential because the monarchy was limited in what it could do. Such restrictions were not evident in the realm of business, demonstrating another difference between Spain and England. Private companies were able to fund more expeditions, develop more accumulation of wealth, and thus fund more voyages into the New World, a flexible approach that the Spanish crown lacked.
Another difference between both modes of exploration can be seen in economic profit motive. While there were other elements to the exploration process of both nations, developing wealth was intrinsic to both nations' attempts. The Spanish model of the Conquistador was rooted in "God, Gold, and Glory." This was seen in how wealth was determined by the Spanish explorer. The ability to discover gold and silver was how wealth was established. In the short term, this was quite profitable. However, over time, such a metric was challenging to sustain because gold and silver were finite resources. They could not be grown, and once the precious metals were extracted, little chance of replenishment remained. The English metric of establishing economic profit was a bit more flexible. The English made use of raw materials such as sugar, rice, and tobacco and were able to develop trade patterns of goods and services. This approach yielded greater long term vision because they could constantly be traded with other partners over time. Gold and silver were finite, but for all practical purposes, crops and other natural resources could be traded for a longer time. This helped to sustain English colonization profit for a longer time than the Spanish model of exploration.
In another way, this reflected a primary difference between both models of exploration. The Spanish Conquistador was mercenary, to a great extent. They sailed for the Crown, but they really sailed to enhance their own sense of profit and their own "glory." When the profits dried out, their mission shriveled. English colonization was not done out of such an individualistic point of reference. The English colonization of the New World was done to establish a long term approach of business growth and accumulation of wealth. English attempts at colonization were not seen as so "swashbuckling," but rather a methodic and deliberate means to generate English community and presence in the New World. It was also done to expand the outreach of businesses in the New World. The English attempts at colonization were seen as more "long term" in the idea of establishing roots over time.
The "God" aspect of Spanish exploration helped to establish another difference between both modes of advancement into the New World. The Spanish zeal to convert into Christianity was vital to their exploration attempts. For example, Columbus makes repeated voyages into the New World with religious friars in order to convert the indigenous people he encounters. There was a fervor to spiritual conversion that was distinctly characteristic in Spanish colonization. This was not as evident in the English attempts in North America. The primary means of establishing colonies was long term profit and the role of spiritual conversion was secondary, if that. English settlers viewed indigenous people with the same disrespect as their Spanish predecessors. However, they simply shunned indigenous people, not focusing their efforts on conversion and the violence that often accompanied it. This represents another difference between both modes of exploration.