The British Rule affected the city of Bombay in many ways. The first governor of Bombay, Sir Gervase Lucas, was appointed by King Charles. In 1669, the power was transferred to the British East India Company. During this period, major improvements were made to develop the city of Bombay. The first mint and printing press companies were established. The island became the center of commerce. An article about the history of Bombay on Wikipedia mentioned, "The encouragement to the trade in Bombay combined with the Company's military in the Deccan paved the way for the education and economic progress which characterized the city during the nineteenth century."
While Bombay flourished as the center of business in the British East India Company, Delhi was developed into the perfect capital (originally Calcutta) by the British. Soon, Delhi prospered into a city with architectural marvels. An article on the History of India said, "It was evident that architectural developments of New Delhi under British rulers had begun to take shape in the city."
To compare Bombay to Delhi, I'd say Bombay was made the place where the main trade happened. Delhi, as the capital, represented the British.