Rather than using Scheme as a way to teach various areas of computer science, "Teach yourself Scheme in Fixnum Days" purely teaches the Scheme language.
"Teach Yourself Scheme in Fixnum Days" is noted as being outdated in some areas (for example, its introduction to macros using an unhygienic macro system).
"The Little Schemer" does touch on more advanced Scheme concepts, however includes only a weak explanation of them. For more advanced topics, the sequel "The Seasoned Schemer", is required.
Unlike many code practice websites, Exercism requires the user to develop and test entirely offline, submitting only the finished code. This promotes familiarity with essential tools and workflow, not just the bare language.
Rather than merely test for code correctness, Exercism uses peer review to improve general programming techniques. Users are encouraged to comment on others' solutions, and refine their own based on feedback.
It's best to have at least a basic understanding of programming before tackling the exercises on exercism.io. You also have to know how to set up your development environment, as you will be coding everything locally (versus websites that provide you an editor right in the browser).
The layout of "The Scheme Programming Language" sets it up as an ideal reference book, making it easy to find specific concepts which are then explained at length.
"The Scheme Programming Language" is better suited for use as a reference. As an introduction to the language, the dry writing style and lack of exercises make it less-than-ideal for information retention.