I think I've tested all the major podcasts app out there, paid for their subscriptions etc... The one that was clearly over the others has always been Pocket Casts. I'm also a subscriber of https://play.pocketcasts.com, their web platform. I just love them. I'm really happy that they've made the money they deserve (or I hope they did anyway).
That being said, I don't feel confident at all that NPR will now respect my privacy as much as Pocket Cast, the company. I'm really scared that NPR will change the app like all those media companies do when they acquire something good - that is transforming the tool into an ad machine, or at the minimum something to track users.
Despite the blog post where they announce that nothing will change, I hope Pocket cast's team will continue their good work and resist the pressure of a media company.