Which passport is better, USA or UK?
You can visit any country you like on either passport but when you’re on holiday in the EU you can move much more easily on your British passport then your American one. American citizens are restricted to 90 days as a tourist in any given EU country, as a British citizen & a citizen of an EU member state you can even go to live there if you wish with a minimum of hassle. Outside of the EU the same restrictions would apply to both passports for instance if you were to visit an African country you would require a visa to enter regardless of citizenship.