Swagger and Slate serve two different purposes. Swagger is an attempt at a standardized way of describing a RESTful API (similar, for example, to ApiBlueprint)
Swagger is a JSON based API definition format, which allows for the description of REST APIs.
~ API Design Tooling From Swagger
Slate, on the other hand is a pretty theme for writing nice API docs.
- The two are not mutually exclusive
- Ideally, one should generate your slate documentation from your Swagger API description
The goal of Swagger is to provide a standard upon which others can build extensive tooling (for example: documentation, API explorers, mock servers, code generation, testing utilities etc.). See, for example: Swagger Tooling
More to your question: Some Slate tooling for swagger:
- Here is a link to a Slate themed swagger UI
- Here is a project that generates Slate docs based on your Swagger definition
So the two are not mutually exclusive, but to your direct question: Implementing Swagger will give you more options and greater flexibility (was well as the ability to also generate Slate documentation).