I can't go into great detail about the British side of this, but see one answer in the differences in organization between the Spanish and British empires. I'll focus for the most part on the earlier stages of colonization.
In the Spanish overseas possessions, colonies were built with their own viceregal administrations that answered to the Crown but retained a high degree of autonomy vis-a-vis the metropolis – in part due to the distances involved and related difficulties of communication at this point in time. Mixing between Spaniards and indigenous people was part of colonial life from the conquests onwards. In contrast, the British looked rather to building settler colonies with a focus on extracting resources for use in the metropolis. Relations with the native population were tabooed and (as far as I know) rather uncommon. Another difference was related to the economy, as the highly monopolized Spanish economic system, with all trade from the colonies running through Cádiz/Sevilla, was not adopted by the British.

Anthony Pagden (in Lords of All the World) has examined the discussions on Spanish, British and French empire, and highlighted how contemporary theorists of empire followed developments in the respective other states closely: Putting it briefly, a main justification for Spanish colonization was connected to the empire's extraordinary size (under Charles V, and under different circumstances under Philip II); this was in turn connected to the emperor's mission of bringing 'civilization' by way of the Catholic faith to his tributaries. Pagden then traces the beginnings of the Leyenda Negra through British and French writers, who underlined the extreme violence committed by the Spaniards (supposedly extreme in comparison to their colonial rivals). Lastly, he shows how these intellectual discussions influenced the later (British & French) empires' differing justifications of conquest and empire, focusing rather on their right to “unoccupied lands” overseas, rather than the Spanish religious justifications. In these different ideologies behind colonization we can find, I think, an explanation for the different organization of the earlier and later empires, taken together with economic considerations. I summed up some of Pagden's main points here, but the whole work seems very interesting for your question.

Having said this, I would like to add in two ways to your initial premise. Firstly, as you rightly point out, the Spanish initially confirmed many indigenous nobles in (newly created) high administrative positions, and confirmed traditional positions in the 16th century. Nonetheless, the traditional systems of tributary relations were disrupted, and a main reason for retaining native nobles was simply that the Viceregal authorities remained dependent on them at first – for understanding earlier organization forms, but also as the Spanish were still in a small minority. This changed towards the turn to the 17th c. (in connection with various factors, among them the indigenous demographic catastrophe), with the highest posts remaining in hands of Spanish-born people, and with mestizos and especially creoles (of Spanish descent) taking over many of the native titles and possessions. This coincided with a change in Crown policies that started to disfavor both indigenous and mestizo people stronger than before, reflected e.g. in laws against indigenous ordination and writings on native religion. A good starting point for researching these developments would be Serge Gruzinski's Conquest of Mexico.

Secondly, especially looking towards the 18th c., Britain did follow a policy of retaining native nobles in their positions and co-opting their political influence for conquest and administration – one good example of this would be India (as mentioned by The_Manchurian). As you seem to be asking about earlier empire-building this would be another topic though.
Hope this was helpful!

Actually, in some places they did. In India, many Maharajas were allowed to continue ruling their lands, as British protectorates. In addition, in many places the British made treaties with what they referred to as native "Kings" or "Lords". However, in other places, this didn't really happen, because the social structures were too different, and so did not appear legitimate in the eyes of British culture and law. Interestingly, some leaders managed to put their own ruling traditions into terms the British understood, so as to gain legitimacy. Possibly the most successful were the rulers of Thailand, who projected themselves as European-style monarchs, and made out that they were the feudal monarch of nearby areas, in a European style, rather than the patron of a web of tribute networks. This caused Europeans to see the area as a unitary state led by a legitimate monarch and so it would be against international norms (ie European norms) to conquer it (of course, it certainly helped the Kings of Thailand that both France and Britain found it useful as a buffer state between their Empires!). Then, of course, there were leaders that the British didn't really see so much as their equals ("tribal" chiefs) but still dealt with through treaties, which they... sort of respected. The central government tended to respect them more than local colonists.

As to why they didn't intermarry with local nobles, well, this was mostly a matter of racism and social position. Britons in India would often, during the late 17th and early 18th century, marry Indian women, but not normally noblewomen, because Indian nobleowomen were only supposed to marry caste equals. In the later 18th century, this became less common due to a)the rising influence of racism, and b)the increased amount of western women in India. Now, I mentioned that Indian Maharajas didn't want their daughters marrying British merchants or adventurers, but what about noblewomen? Well, frankly, British noblemen didn't want their sons or daughters marrying Indians, who they viewed as inferior.