What is one advantage of using Apex Web Services over Salesforce APIs?

The choice highlighting that Apex methods can encapsulate complex logic accurately reflects a significant advantage of using Apex Web Services. Apex allows developers to implement intricate business logic that goes beyond the capabilities of standard Salesforce APIs. This means you can create tailored web service methods that handle specific requirements, which are particularly useful when standard API operations are insufficient for the business needs or when custom processing of data is necessary before returning a response. Through encapsulation, Apex Web Services can perform complex operations such as validation, data manipulation, and integration with external services all within a single method, providing a powerful way to streamline and manage custom logic.

In contrast, while flexibility and manageability of methods may apply to some extent, they do not capture the full depth of what makes Apex stand out. Additionally, Apex Web Services do require a significant amount of coding, especially when compared to the more straightforward implementations typically associated with Salesforce APIs, which are designed for ease of access and use. The range of data types that can be accessed doesn't particularly exceed Salesforce APIs in a meaningful way, as both methods generally support various standard data formats.