Banshee – It was the default on Ubuntu for a bit. (Eventually they went back to Rhythmbox). Reasons to try it include it are it manages videos too, including syncing movies to other devices.
Rhythmbox – It’s the default on Ubuntu. It’s a solid well-built music player. It’s very clean for packing in so many features.
My Recommendation: Stick with Rhythmbox unless you want the video management. This post is just a Banshee overview.
The Online Media seems like it just opens the websites in it’s internal browser and provides some integration to connect to it. It does make it easy to discover a podcast, but Radio presets are not auto-filled. For actual music management it seems quite similar to Rhythmbox except that it shows album art by default. There are many plugins available for both to extend what they can do.
I’ve run into a number of bugs while using Banshee, I can’t exit the program on my desktop. I guess it’s designed to integrate with Ubuntu’s indicator applet and minimize to it by default? It also did crash in my testing. I think it is related to the fact it needs a full browser for the Online Content.
Banshee’s underlying technology has been somewhat controversial in the open source world. It’s uses Mono which is an implementation of Microsoft’s .NET/C#. I considered it a bad idea because we have so many great programming languages that are community driven. Why do want to accept Microsoft as a though leader? One of the other big reasons was that it wasn’t as efficient memory wise. Banshee back in the day was certainly guilty of this. But this recent release shows that they can make a mono based memory efficient music player program