I've had this in the queue for a few days and now -- thanks to Lifehacker (Sweet Setup agrees) -- I see no better time to post this than today. But if you're wanting to listen to podcasts on an iOS and/or Android device, then you'd be wise to just go ahead and download Pocket Casts.
The app, itself, puts it simply: "Pocket Casts is a powerful Podcast manager for iPhone and iPad."
Pocket Casts contains just about every major feature that you'd expect out of a podcast client, as well as delivering on a beautiful design experience with very smooth transitions.
The biggest, and best, feature to me is the sync/backup functionality. I use my personal and work phones, as well as my iPad and Nexus 7 to listen to my 60-plus podcasts. Which device I use depends on quite a few variables, but I never have to worry about what I've missed or where I left off because the sync capabilities have kept me in place every time.