IS Singapore zoo really the best zoo in the world?
Defining "the" best zoo(s) is a matter of constant dispute among zoofans as it's commonly an aspect of individual taste, influenced by personal experience and expertise as well as the individual cultural, social and academic background. It depends on many aspects, may it be the quality of husbandry, zoo design, architecture and history, diversity and quantity of kept species, visitor amenitities, staff satisfaction, profitableness, research and conservation impact, location of the zoo and so on and on, all which are valued differently. Some ZooChatters love old-fashioned zoos with a focus on species diversity and zoo history, while others prefer zoos offering modern entertainment options and animal theme parks. Therefore, Anthony D. Sheridan's or others' rankings of zoos are often highly debated among zoos and zoo fans. Reviews on Tripadvisor and other travel websites offer a more generalized rating of the individual zoo, often influenced by the (very) personal expertise (or lack thereof) of the reviewer.
As you can see, it's not easy to answer your questions. As a zoo in the Tropics, Singapore Zoo has different preconditions to maintain and represent species than zoos located in different climate zones. This greatly influences husbandry, landscape design etc. No zoo is the same, even though general issues and problems are shared among zoos all over the world (like escaped animals, underpaid staff or unruly visitors).
As for which zoo to visit in the UK or US, expect several replies, with some (Chester, Durrell Wildlife Park, Bronx Zoo, San Diego Zoo etc.) more likely to be mentioned and recommended than others for the reasons mentioned above.