A podbrowser, on the other hand, isn't designed to download anything automatically, but rather show every episode available on a given stream so that the listener may download any or all shows as desired.
They both have their strengths, and while I don't think any real podbrowsers exist, many podcatchers can be configured to offer podbrowsing capabilities.
A podbrowser is handy when you've just subscribed to a show that you've ended up linking. You can then search through and download all of the old episodes. If you were using a more traditional podcatcher, you would probably only have access to the last 5 or so shows and would have to stomp through the show's website to find the rest.
A podcatcher, however, is good if you have no interest in older shows such as when you're just looking for the latest episode of a show you're already subscribed to. Podcatchers will grab that episode for you while you sleep and many will also put it on your digital player.
To each their own...