when should you use a CDN versus client-side caching, maybe it depends

Hey everyone, I'm trying to figure out the best caching strategies for our really busy web app. We've got tons of static files, plus some content that changes a bit. My first idea is to shove most of it onto a CDN. But, I'm curious if there are times when leaning more on the browser's cache would be better, or even faster. What do you guys usually do to pick between these options, and what do you think about the pros and cons?