I may not be drawing too much upon the period 1600-1800 specifically: however, I feel the reasons for the worldwide dominance of England, originally, and later Great Britain as a whole were similar to those of the late 19th and early 20th century. Therefore, I feel some of the main issues within the realms of political science tie in with your fascinating question.

Geostrategically, England was able to concentrate on its navy once all domestic (British) conflicts had been resolved (the English even managed a Civil War). Unlike the Spanish, who were threatened by their borders with France, and close proximity to other Mediterranean powers. This was due to the fact that Britain was not only an island, but also an island surrounded by a particularly stormy set of seas. This meant, therefore, that even if an invasion force were assembled, it not only faced the English navy but also the seas of the British Isles (especially deadly in the 1600-1800's, for the wooden vessels of the time- The dispersion of the Spanish Armada seems a prime example). Therefore, Britain was able to develop itself freely, with a reduced fear of invasion.

A strong navy was, and arguably still is (see Chinese naval bases in the pacific oceans), is one of the key criteria needed to assert control/influence overseas. However, the English/British were able to build their navy for another reason- national security. The fate of English/British navy was intertwined with the fate of the ruling regime as a whole. A strong navy was essential to defend the British Isles, not a strong land force. This can be seen in the reluctance of any of the English/British regimes to develop a large land army, as it was not a productive use of resources. Therefore, Britain was able to effectively kill two birds with one stone.

This does explain British dominance after the fall of the Spanish empire. However, it does not explain how the British succeeded the Spanish directly. I seemingly remember a lecture by an historian, his name escapes me, that the reason the British succeeded in outlasting the Spanish was by using all the stolen gold they acquired from them by piracy. This seems rather simplistic, as a sole reason, but it could be just one of many reasons. I feel that the reasons listed above helped to make up for the gap already established by the Spanish over the British.

However, perhaps a better explanation for the rise of Britain at the apparent expense of the Spanish, was due to the industrial revolution in the 19th century. Britain led, and (I'd be fascinated to see some statistics if anyone knows of any to hand) Spain withered. I do think this could have been the final nail in the coffin for Spain. Spain never truly industrialized in the 19th century, and this accounts for its fall from Great Power status- Great Powers were ranked by their industrial power, as well as the prestige of Empire (Germany are a prime example: they never really attained a great empire of territorial possessions, but were perhaps on a level with Britain as the worlds greatest power at the turn of the 20th century due to the scope of their industrialization.).

Industrial power was increasingly a pre-requisite for maintaining a global empire. With the introduction of steam powered battleships, and later dreadnoughts, Britain capitalised on its advantage by using its industrialization to develop itself as the worlds greatest sea power. Spain seemingly simply failed to adapt itself to the modern game of of Great Powers- the reasons for this could be multiple (the hindrance of the living in an overly religious society, inefficient statecraft, lack of natural resources compared to Britain, or the stresses and strains of continental security).

One thing to bear in mind is that a popular theory in political science, is that of the rise and fall of world powers. Citing examples of Britain and Germany in 1914, and the USA and China today, the theory presents the idea that whenever there is a rising and declining power dominating worldwide affairs, conflict is inevitable. Could the case of Britain fall into this theory? Spain, the established but tiring power, competing against a new and surging power in England (initially, GB later), seems to fit?

This is my first post here on the site, so take it easy on me ;)