I’ve never used Antenna Pod, but I’ve used Podcast Addict for more than a decade, I’ve paid for the pro app, and I’ve been really impressed by what it can do.
I like to have many podcasts downloaded to my phone, and Podcast addict has really granular controls for what to download and keep for how long, in the general case, and for each podcast you can dial in custom settings, for example not auto-downloading or deleting. It helps me have plenty of audio to listen to at all times without blowing up the storage on my phone.
The various automatic playlists for downloaded episodes, new episodes, and recent episodes are also very useful to me.
I’ve found the developer to be really nice and he will personally respond to bug reports and support requests if anything doesn’t go as planned.
Does pine pods do syncing?