Hi u/Pokonic
Sincere apologies for the late reply, I am away on a research trip and my time is quite limited.
Note: I use the term "native" here not in the derivative sense but to describe a population group that is of domestic origin to the country in question.
First thing I think we should tackle is the enormity of the question you are asking. Africa is massive and the first thing we should note is that each and every British colony/territory was treated differently by Britain depending on its requirements. The native populations, too, reacted differently to the presence of colonials depending on the policies enacted and the culture of the native population. As such, there are too many factors to consider when answering this question in a reddit thread so I will link articles which should answer your question at length - though I should also add that it won't be answered specifically as I don't think a comparative study answering your specific question exists.
That being said, I found a thesis that does do a comparative study using wages and GDP, but it focuses on 1880-1945 which might still be of interest.
To illustrate the scale and differences I was talking about: there were approx 21 British colonies in Africa at the height of the European presence in Africa, and by the 1950's two of them had been granted independence (South Africa and Egypt) with the rest swiftly following between the 50's - 80's (mostly the 60's).
South Africa was unique in that regard as it had been independent since 1910 and had a strong mix of British, Dutch, and German influence in its bureaucracy and how it treated its native population. It and Rhodesia (Zimbabwe) were also the only British colonies released into white minority rule, as opposed to the other colonies which were released to black majority rule. Rhodesia and South Africa, though, eventually gave way to black majority rule.
Racist practices still existed as a hangover from slavery (which had only been abolished a few decades prior) but the black populations were gaining momentum in their political enterprises.
After WWII, many Nazi members and sympathisers fled Germany and some ended up in South Africa where they began to influence the political structures there, and Apartheid was implemented by 1948. The living conditions of Africans in South Africa had been slowly improving before this, but after 1948 it began to plummet again.
Three really good articles detailing the change and conditions in SA society can be found here:
The History of Separate Development in South Africa
Black living standards in South Africa before democracy: New evidence from height
Colonial institutionalisation of poverty among blacks in South Africa
South Africa and Rhodesia were unique in their influence in this regard (although Botswana and Nambia were equally interesting due to their proximity to SA and Rhodesia, their involvement in the conflicts that arose in the 60's, and Namibia as a former German colony that became a South African protectorate until it's independence.)
Moving away from South Africa, as I said before, each colony would have had different levels of living standards. For example, some colonies were earmarked to produce educated manual labour and the education programs reflected this: The Education of African Children in British Colonies, 1910–1990
Whereas others were more about resource extraction and social integration for easier colonisation, for example this article says:
In West Africa the impact of British rule was more dramatic. The British had been heavily involved in the West African slave trade in the 1700s. The trade was abolished in the early 1800s and the British put a lot of effort into trying to wipe out slavery and the slave trade in all of Africa. This changed Britain's relations with West Africa. British merchants and traders developed close links with the rulers of the many different nations on the West Coast of Africa, such as the rulers of Benin, Dahomey and Asante. These nations provided Britain with gold, luxury foods and many other goods.
Throughout the 1800s British traders and politicians became increasingly involved with the leaders of these nations. They made alliances and helped out some nations in their wars with others. By the 1880s West Africa was dominated by Britain. Local chieftains ruled their own peoples using their own customs. However, they paid taxes to Britain.
As in Egypt, the families of chieftains often gained from British rule. They adopted the English language and British clothes. They were educated in Britain. They took up some posts in the civil service in West Africa, although the senior posts were always taken by British officials. For ordinary West Africans, British rule brought major changes to their everyday lives. The British brought in a system of owning, buying and selling land, which meant many Africans had to pay rent. This meant that instead of growing crops for food, they had to grow crops to sell (to pay the rent). These were usually crops like rubber or cocoa. They also found that their traditional crafts were sometimes destroyed by competition from goods produced in British factories.
Unfortunately I don't have the space or time to delve in further, but I think these articles should give you a great lead to answering your question:
Colonialism and development in Africa
The Colonized as Child: British and French Colonial Rule
Living Standards in British Africa in a Comparative Perspective, 1880-1945
The Education of African Children in British Colonies, 1910–1990
African Economic Development and Colonial Legacies
Analysis of Colonialism and Its Impact in Africa
Living in the British empire: Africa
And then, to think about how the colonies affected British society: British Colonialism and Social Change in the Metropole
Hope that helps!