What are the core differences between service worker and AppCache. What are the pros and cons of each and when to prefer one over another .
The primary difference is that AppCache is a high-level, declarative API, with which you specify the set of resources you'd like the browser to cache; whereas Service Worker is a low-level, imperative, event-driven API with which you write a script that can intercept fetch events and cache their responses along with doing other things (like displaying push notifications).
The pros and cons are largely a function of API design: theoretically, AppCache is easier to use, while having more limited use cases; whereas Service Worker is harder to use, but is more flexible.
Nevertheless, AppCache is considered hard to use in practice due to poor design (see Application Cache Is A Douchebag for a list of design issues). And it has been deprecated, so it is being removed from browsers (per Using the application cache).
Thus the only reason to prefer AppCache is to offline an app on browsers that don't yet support Service Worker, as Kenneth Ormandy recommends in Don’t Wait for ServiceWorker: Adding Offline Support with One-Line.
Compare Can I use Service Workers? to Can I use Offline web applications? to see the differences in browser support. But note that browsers that support Service Worker, like Chrome and Firefox, are removing support for AppCache, so you'll need to implement both to offline your app across all browsers that support either standard.