How was the English empire different from the other European colonial empires? How was it the same?

First of all, the empire which, at its height, ruled almost 25% of the world's population was the British Empire, not the English Empire—although, it was often noted jokingly that it should really have been called the Scottish Empire, as it came to be very much dominated and run by high profile Scots (more on this in Michael Fry's excellent book, The Scottish Empire).
There were many similarities between the British Empire and other colonial Empires in terms of how they invaded and captured their colonial nations and sought to eradicate local traditions. All colonial empires effectively performed similar acts of subjugation: stealing resources from the countries they conquered and asserting their supremacy, based on extremely racist logic, over the local populations. However, the British Empire was older, longer-lasting, and far larger than most of its "competitors," which had an effect on the way it ruled. Because the Empire was so large, it tended to exercise more indirect rule in terms of having protectorates which, to an extent, governed themselves under the protection of Britain, with a small number of British advisors in-situ to keep control. Some of the administrations set in place by the British Empire were, to a considerable extent, retained by the countries long after independence—as, for example, in India.
The British Empire also outlawed slavery early in the 19th century, and attempted to take a strong stance against the barbarism perpetuated by, for example, the Belgians in the Belgian Congo. In the British Empire, discrimination fell more along arbitrary class lines than race lines: there were sitting Indian and black members of parliament in the UK from the late nineteenth century, because money was what truly mattered, rather than race. In a sense, Britain's entrenched class system served to protect the wealthier pre-existing ruling classes of some of its colonies from the worst excesses of racism.