I haven't lived in Colchester (but been there a few times), so my comment is a general one (know Manchester very well, have lived there and have family there now).
Manchester is a city, of over a million including surrounding towns (Greater Manchester). It's very multi-ethnic and cultural, and as an Indian you should feel at home there, though the majority of Asians are Pakistanis and Bangladeshis, with most Indians of East African origin. People are quite friendly with a typical Northern openness. Cost of living is lower than in the South East, esp rent. Weather is generally colder and wetter. It's one of the biggest student cities in UK and choice of amenities is vast. It attracts students from all over the world. It has good rail, road and air link with the rest of UK, Europe and the world, with Manchester Airport a hub for people living in Northern England.
Colchester is a former garrison town (close link with the army). It has seen a lot of changes with new developments, shopping centres and housing areas, often on former army bases. London is about an hour away and Stansted Airport is handy for cheap flights to Europe. It has some ethnic population but not particularly high - around 5% compared to Manchester's 30%. As an affluent South-Eastern town, cost of living is significantly higher, maybe 40-50% higher than Manchester. Both Colchester and Manchester go back to the Roman times. Both unis have good academic reputations.