Apple’s Podcasts makes it super easy to find and subscribe to podcasts as well as customize the look. You can create Stations, lists, and can even set it up so after a podcast is listened to, it disappears off your app.
Pocket Casts is clean and easy to use, similar to the iOS counterpart. Swipe to the right to find the controls, and discover new podcasts with the discover button. You can also use their search to find a specific show. Similar to iOS’s Podcast app, Pocket Casts will let you customize your app interface by organization, in any way you’d like.