This speaks to a bit of a popular misconception: historians don't really do 'cost-benefit' analyses. It's not just that many historians find such an approach unethical, since it tends to favour the powerful (it's easier to estimate the value of a bridge built by a colonial power than the value of the lives lost building it), but because it's almost completely impractical to boot.
For one thing, cost-benefit analyses are extremely culturally contingent. Do we take the view that the extension of Western style private property rights into India were a benefit? Or, conversely, the Soviet Union's expansion of state socialism into Eastern Europe? That's obviously going to depend entirely on the historian and the historian's audience. We can instantly see that there is no 'fair' basis for analysis there- the one approach is going to excoriate one empire and excuse a second, and already we have begun to assume that empire is something to be looked at from the perspective of the imperialists.
For another, historians don't commence a study by setting out to decide whether something is 'good' or 'bad.' Historians seek to examine what happened, why it happened, how it happened. As a historian of Australasia in the late nineteenth century, I will often talk about policies or cultures that I will label with terms such as 'white supremacist,' 'Anglo-Saxonist,' or 'racist,' because that is a matter of simple factual description. I do not use the term 'evil' for, say, the White Australia policy- because 'evil' is an abstract moral judgement. Instead, I can simply describe the paranoia of its supporters and the lives that were destroyed by its implementation.
Equally, just as I do not need to use the word 'evil' I also am under no obligation to then ask 'but was the harm of the White Australia policy balanced (in whatever sense we want to use that word) by the benefits of other policies?' For one thing, that necessarily implies linkage- that any good government policy at the time necessarily had to be carried out in conjunction with racial exclusion laws. But it also says nothing about White Australia- if you are a Solomon Islander who has lived in Queensland for twenty years with your family, and in 1906 you are forcibly deported under the Pacific Island Laborers Act 1901, does it matter to you if the Commonwealth of Australia is also a leader in workplace relations laws? How on earth would any 'Cost-Benefit analysis' intelligently answer that question?
Another problem is that looking at imperialism through the lens of a 'cost-benefit analysis' requires an approach that's fundamentally based on counterfactuals. For those who don't know, counterfactuals are essentially 'what if?' questions. A corporate consultant can make a cost-benefit analysis of a business decision because they can measure it against other firms who did or did not take such a decision.
You cannot do a cost-benefit analysis of British imperialism in Australian history, for example, because we only have one example of Australian history. We can't compare it to any other continent in the South Pacific, inhabited for at least fifty thousand years with hundreds of different cultures and nations that was not colonised by a European power. How would we begin measuring the benefits? Benefits for who? Benefits for the British settlers? Benefits for the indigenous Australians and Torres Strait Islanders? The standard imperial apologia in Australia is that, yes, those communities still suffer worse health-care outcomes than any other group in the country but at least there are Western hospitals, right? Leaving aside the obvious rejoinder that vast amounts of indigenous health issues are directly attributable to colonisation, such a defence also assumes that the only way there could ever be a functioning hospital in Australia in 2021 is if a colonial power had invaded and built the necessary infrastructure.
The thing is- even if that's true, it's unknowable! So we can't possibly draw any conclusions from it.
In summary: the question's not really answerable as written. God knows, I or any other specialist can talk to you about the 'unmitigated disaster' of British rule in various cases, but that doesn't actually bring us any closer to being able to answer it as a comparative question.
I can attempt to answer this question from the Indian perspective. The historiography surrounding the period from 1600-1947 in the history of India which presents the history of the English trading company, the gradual decline of "native" powers in the subcontinent and the eventual and gradual territorial annexation of nearly the entire subcontinent by the Company Bahadur (British East India Company), took shape since the beginning of the Independence movement in the Indian subcontinent. The ideological underpinnings of the then emergent and mainstream, nationalist-Marxist historiography served to present the history of the Company's rule and the British Raj, as one which was fundamentally antagonistic and alien to "Indian" interests and people. Among the many nationalist-Marxists who laid the foundation of this historiography in Indian history, were Dadabhai Naoroji and Romesh Chandra Dutt. Among the most enduring legacies of this school of thought and approach to writing the history of Company rule and the British Raj, has been the attempt to quantify the cost of the colonial experience, to put a number to the entire period from the beginning of the Bengal Diwani of the Company in 1765, to the end of the British Raj, as an estimate of the total negative impact/cost of the colonial experience for India (used for convenience in place of 'Indian subcontinent') called otherwise as the "Drain Theory". The argument had immediate appeal for those seeking leading the independence movement, and the rhetoric that further propagated and popularised this methodology and approach, weaponised the numbers produced by these quantitative analyses. Curiously, neither the methodology nor the numbers have been conclusive and the only constant and discernible throughline argument of the approach is that 'British rule was disastrous to the subcontinent, in monetary and qualitative terms', with the methodology providing the data for the former and the latter being a conclusion based on the data. An example of this approach and a proponent of the drain and the inevitable negative outcomes of the British rule, Irfan Habib, in his 'Studying a Colonial Economy - Without Perceiving Colonialism', Modern Asian Studies,1985, pp. 375-6, quotes a figure to the tune of Rs. 1,355 million for the drain in 1881, in 1946-47 prices.
As a more recent example, we have the work of Prof. Utsa Patnaik, who is popularly quoted as having quantified the drain between 1765 to 1938 as $45 trillion USD. We can first look at how the number has been arrived at, namely the figure of $45 trillion. Here I'll be using quotes by Prof. Patnaik, in her own article, in the "Monthly E-Newsletter – Amity Business School, Volume V, Issue I, October 18", titled "How the British Impoverished India"
After decades of research I find that using India’s commodity export surplus as the measure and applying an interest rate of 5%, the total drain from 1765 to 1938, compounded up to 2016, comes to £9.2 trillion; since $4.86 exchanged for £1 those days, this sum equals about $45 trillion
There is first the issue of using export surplus as the measure for appropriation. Before approaching which, I must draw attention to the seemingly arbitrary 5% interest rate, for which we are given no explanation. There is then the use of exchange rates from pre-1938, passed off as $USD in 2016, expressed in terms of it's value in comaprison to the £ in the same era, while the exchange rates for the two currencies were drastically different in 2016. This is, not reflective of serious thought being applied to this evaluation. To add to that, according to Tomlison, B.R.The New Cambridge History Of India III, The Economy of Modern India, 1860-1970, 2003, p. 13-14
The size of the unrequited transfers, those needed to meet the 'Home Charges' (the administrative and military expenses of the Indian Government in Britain), was small, running at around Rs 20 million a year, less than 2 per cent of total export values at the end of 1913.
[ Source : India's International Economy in the Nineteenth Century: An Historical Survey Author(s): K. N. Chaudhuri, Modern Asian Studies, Vol. 2, No. 1 (1968) ]
Prof. Patnaik sheds light as to how she arrives at this conclusion in the article :
The Secretary of State for India in Council, based in London, invited foreign importers to deposit with him the payment (in gold, sterling and their own currencies) for their net imports from India, and these gold and forex payments disappeared into the yawning maw of the SoS’s account in the Bank of England. Against India’s net foreign earnings he issued bills, termed Council bills (CBs), to an equivalent rupee value.
Description of such bills of exchange as "appropriation" by the British government, is highly contentious and doesn't seem to be based in any evidence. The sale of Council Drafts was a convenient tool for the management of Indian currency, exchange, and finance. Usually, India ran a surplus on trade account, yet, payment had to be made in sterling to meet the ‘Home Charges’. The Secretary of State in Council invited tenders for delivery of sterling in London against payment in rupees from Government funds in India. The Act XVII of the year 1835, declared the silver rupee of 180 grains troy, 11/12ths fine, as the sole legal tender currency of British India. Furthermore, average production of silver rose from 1.34 million kgs. during 1866-70 to 1.97 million kgs. during 1871-75 and further to 2.86 million kgs. during 1881-85, gold output declined from an average of 0.20 million kgs. during 1866-70 to 0.17 million kgs. during 1871-75 and further to 0.15 million kgs. during 1881-85. This severely depreciated the value of the Indian rupee. To add on to the problems of the Government of India, the payments for the "Home Charges" of the Government, being interest on debt, pensions, payments to the War Office, cost of Government stores, etc. increased, and these had to be made in sterling. The government flirted with a gold standard, and a committee was setup for the same purpose under Lord Herschel, the Lord Chancellor, in October 1892 by the Secretary of State, yet the growing silver shortages, explain the necessity for the Council Drafts as a means of exchange.
[ Source : Money, Prices, and Economic Development in India, 1861-1895, Author(s): John Adams and Robert Craig West, Source: The Journal of Economic History, Vol. 39, No. 1, The Tasks of Economic History
Transition from Indian to British Indian Systems of Money and Banking 1800-1850, Author(s): Amiya Kumar Bagchi, Source: Modern Asian Studies, Vol. 19, No. 3 ]