@Gaby I confess I've never used Castro or Pocket Casts - but only because Overcast has worked flawlessly, with the annual subscription, for 4+ years for me. Synchronisation between multiple devices is the key for me - including the desktop/web interface (which I repeatedly hear Marco saying hardly anyone uses - I do!). Everything works for me in Overcast.
I keep hearing about podcast queue/inbox management in the other apps but don't really get it. I generally subscribe to 10-15 podcast streams and have no problem deciding what I want to listen to and when I want to listen to it. Overcast allows me to manage this perfectly (with a very usable interface) and keeps downloaded episodes until I'm ready.
And I agree with you about Apple Music!