I had learned (from Adrian Cantril's/LA's 2019 SA Pro course) that Redshift Spectrum would use one's own Redshift cluster to provide more consistent performance than is available by leveraging the shared capacity which AWS makes available to Athena queries. I appreciate this information might only be useful for the exam, I didn't find his argument convincing.
I wrote this answer because I wasn't satisfied with the leading answer's treatment of Athena outperforming Redshift Spectrum. The rest of that answer is good and I do not mean to directly copy any of that here (without references it hadn't registered with me when I wrote this).
I (again, based solely on my hands-off research) would choose Spectrum when the majority of my data is in S3, which would typically be for the larger data sets. The recent RA3 instances seem to overlap this niche though. So I say Spectrum is most suited to where we have long term Redshift clusters that, being OLAP nodes, have spare capacity to query S3.
Why would you use your own estate to perform the queries that Athena would do without such an investment from you? Caching, where it fits. And consistent performance, if I am to believe Adrian Cantrill more than Jon Scott. This made me suspect RA3 might be edging Spectrum out; that and the lack of decent literature on Spectrum. Why would Amazon offer a serverless product in Athena that outperforms Redshift Spectrum which is more expensive? This is how they are choosing to deprecate RRS. I can't believe Spectrum is deprecated so must offer this answer to contest this. Just look at https://aws.amazon.com/redshift/whats-new/.
I think the picture below (from https://d1.awsstatic.com/events/Summits/AMER2020/May13SummitOnline/Modernize_your_data_warehouse.pdf) is fairly clear that compute nodes are influential here, and perhaps contrary to @JonScott's valuable insights above.
One final big difference is Athena is limited to IAM for authentication, as depicted in this reinvent 2018 (ANT201-R1) slide: