This is a good question. The Empire controlled a vast amount of land at its height. But control of it in practice differed from region to region.

The best-off were probably the Anglo-Saxon settler colonies in the Americas and Oceania. This of course resulted in the displacement and extermination of the native peoples of these continents.

The second would be the establishment of protectorates over existing governments in the Middle-East and Asia. This is done through both diplomacy (the Arab gulf) and conquest/coercion (India). In many cases, the British elected to keep the existing governmental structure in place, but kept advisers or 'Residents' to give the ruler advice, essentially as puppet rulers while the appointed envoys controlled economic and foreign policy of these nations.

The last however would include the African protectorates and colonies, as well as the artificial Middle-East divisions carved out of the Ottoman Empire. Combining and splitting ethnic groups into artificial boundaries is the root cause of much of the violence throughout these regions to this very day. The French, Portuguese and Dutch of course share the same blame.

For education; British colonial education were driven by the actions of independent religious missions. Otherwise, there is the argument that there was some form of 'cultural' uplifting in the colonies. But this is countered by the formation of unstable governmental structures left in the wake of decolonisation in Africa. Decades of instability and civil strife has wiped away the advantages of 'uplifting' native Africans.

Colonial Policy; British colonial policy always had a focus on maximizing benefits for the Home Isles. This is either through establishing trading monopolies such as through the East India Company or controlling the foreign and economic policy of the various protectorates. A focus on cash crop plantations is also one result, with commodities gaining greater traction as the Industrial Revolution continued. We can at least establish that the British Empire's interest were never for the well-being of the natives, unless there was a need to placate the natives to preempt rebellion or revolt. For example, if Bengal survived the British, there would be a continued attempt by the Rajas to modernise and slowly adapt to the imperialistic ventures of the European powers.

A contentious argument would be asking whether British exploitation of its colonial possessions resulted in a better outcome than local elites doing the same. Whether subjugation and control by a local ruler is better than the benign neglect of an appointed envoy. If we use history as a measurement, the conflicting priorities of a colonial administrator and a local ruler leads to a contradiction. Would something similar to the Bengal famine still occur without a British India?

And to the final question. Are the colonised areas better off? This is a subjective question. It depends on what measurement you prefer and what you personally think has a greater weight on the matter. I would think the world would be 'poorer' because the British Empire was more efficient in utilising its colonies. But because much of the wealth flowed back to the British Isles, the natives never benefited. In terms of national development, I'm personally supportive of societal development as practiced by the local population instead of imposed upon the population by a foreign power.

TLDR; So I personally think the British Empire benefited greatly. But the natives, not so much. Artificial countries with lasting instability and conflict, conflicting priorities of local rulers vs colonial administrators and artificially imposing foreign forms of government into a different society are the big arguments against Imperialism. It's the same as imposing democracy on a Medieval society. The most stable forms of government is self-developed and evolved, not imposed.

And here's a somewhat related infographic. http://www.theguardian.com/uk-news/ng-interactive/2014/feb/11/britain-100-years-of-conflict