Scholars often distinguish between 'colonies of settlement' and 'colonies of exploitation'.
Colonies of settlement are characterised by the permanent settlement of large numbers of people from the 'home' country, who see a move to the colonies as a permanent life choice for themselves and their descendants.
They put down roots in the country, they invest in building up a place that is now their home. Their institutions - legal and judicial systems, administrative systems, representative and political institutions, religious and educational institutions - are translated into the new context.
While this form of colonialism is hugely disruptive and detrimental to the native/indigenous/aboriginal inhabitants, it is not experienced as exploitative or detrimental to the settler population. Quite the opposite - they may experience historical connections to the 'home' country as a source of cultural pride, as well as a source of military protection and economic opportunity.
At least as far as the English-speaking white population was concerned, Canada, Australia, New Zealand and South Africa (although the Boer Wars complicated things in the latter case) were largely in this category.
Moreover, because they had transplanted parliamentary institutions, these countries had all achieved substantial self-government by the beginning of the 20th century. When they were ready, at a pace determined by themselves, they progressed gradually, imperceptibly, towards independence, without a war of liberation or any kind of struggle.
In short, these countries did not experience the British Empire as oppressive. If anything, it was core to their national story. Many Canadians distinguish themselves from Americans by emphasising links with the monarchy and the Commonwealth. Australians and New Zealanders forged their national identity (Anzac Day) fighting as part of an imperial force against Turkey in the First World War.
(Also, because of settler roots - even if diluted by subsequent waves of immigration - there was an cultural familiarity. I have to be careful here, because there's a danger of going beyond my field of British and Commonwealth constitutional history into some area of cultural studies, but I think many Australians and Anglophone Canadians would regard Shakespeare, Milton and Dickens as part of their shared cultural heritage, and not as something alien and imposed.)
All of this adds up to a degree of cultural, as well as institutional and political, familiarity, consanguinity and friendship. Some of that settler transfer happened relatively recently, too: as late as the post-war years British people were settling in Australia (as ten pound poms) and in Canada.
Here the situation is different. The climate and environment of such colonies, or the presence of existing sophisticated and technologically developed civilisations, did not facilitate large scale settlement. Instead, the impact of the imperial power on the colony was largely extractive - perhaps to do mutually beneficial trade, but more often to establish monopoly control over markets and resources.
Because there was limited long-term settlement, most people saw such colonies as an opportunity to 'get-in, get-rich, and get-out'. People might spend their entire working lives in the colonial service or in one of the many companies doing imperial business, moving from, say, Bombay (Mumbai) to Mombassa (in Kenya) to Singapore - and then, crucially, retire back to Britain. Their children would be educated in Britain (at boarding schools). Some people did stay and even intermarry (forming, for example, the nucleus of the 'Anglo-Indian' and 'Anglo-Burmese' communities) but these were relatively few in number.
There were was attempt, in those countries, to develop the economy, but these policies not primarily directed to the benefit of the people who actually lived there. For example, when Australians or Canadians built railways, they did do to develop the interior of their countries. When railways were built in India or Africa, it was done primarily for the benefit of the colonial powers (militarily and strategically) or their commercial interests; benefit to the colonised population was not negligible, but it was somewhat incidental.
Likewise, political, administrative and legal institutions in colonies of exploitation were primarily directed towards maintaining imperial rule - there was some real and genuine concern for justice (let's not paint all British imperialists with the 'evil' brush; the reality is far more complicated than that) - but this was subordinated to the needs of colonial administration. For example, there was often a distinction between 'native courts' which settled minor disputes according to (British-mangled interpretations of) traditional or customary law and the courts serving the small resident British commercial / missionary / administrative community. Trial by jury and other procedural rights were often not extended to the 'native' population; instead, various forms of administrative detention could be applied which in the UK (and settler colonies) would have been unlawful.
While the settler colonies had functioning (for white settlers) democracy by the end of the 19th century, the colonies of exploitations had to wait much longer for democratic development. Usually - it's difficult to generalise too broadly, because the pace of change varied a lot - there was a Legislative Council with some elected element (alongside nominated and ex-officio 'official' members) by before the second world war, but universal suffrage to a fully elected legislature to which the government was responsible was often not achieved until a decade or so before independence (1950s) - by which time rancour and the desire for independence were strong.
So these colonies - while not entirely unthankful for having been colonies of Britain (and not, say, France or Belgium) - did experience colonial rule as exploitative economically and repressive politically.
These two very different sets of experiences naturally lead into different post-independence relations. Still, much depends on the process of independence itself. Sometimes post-independence relations got off on a good footing, sometimes a bad one.
The Caribbean colonies are particularly interesting. They were for the most part colonies of exploitation, not settlement. As in Africa, they mostly achieved independence in the 1960s. But they had largely developed workable two-party politics before independence, and crucially - having been enslaved societies, and under British rule for much longer - did not have tribal identities. Their cultures had been largely moulded by centuries of British rule. Their anti-colonial rhetoric was more muted - and indeed many of these countries retain the Queen as head of state and have good relations with the UK.
I don't have time to write much more now.
Jennings, W. I. (1958) 'The Approach to Self Government' (Cambridge University Press).
Patapan, H., Wanna, J. and Weller, P. (2005) 'Westminster Legacies: Democracy and Responsible Government in Asia and the Pacific' (University of New South Wales Press).
Kumarasingham, H. (2013) 'A Political Legacy of the British Empire: Power and the Parliamentary System in Post‐Colonial India and Sri Lanka' (I. B. Tauris.)
Acemoglu, D. and Robinson, J. (2012) 'Why Nations Fail: The Origins of Power, Prosperity, and Poverty' (Crown Publishing Group).