I've been using Podcast Addict as a podcast app on Android, to be honest I'm not unhappy with it either. But I'd like to perhaps try some alternatives to test the water, as I picked it more or less at random.
Basically my only absolute requirement is that it has an option to download the podcasts to the phone - I tend to listen to them in a room at work which doesn't have WiFi (no it's not a typical office!).
In an ideal world the app would also:
i) Be able to migrate my history of listened podcasts from Podcast Addict, and preferably back again.
ii) Have a good UI - in terms of functionality, not modernity. Old-fashioned and clunky's fine if the functionality's good. Material design a big no-no, I dislike it aesthetically and functionally so...