You might find the answer in the threads referring to the volume of undesirables in the UK, many of whom hold British passports (some fake, some real but illegally acquired).
The USA is rather more cautious about whom it allows onto its territory.
Visa requirements are often reciprocal, but as an example, whilst South Africans require a visa to go the UK and most of Europe, UK and EU citizens do not require a visa for South Africa.