Azureus is like µTorrent.

They use Torrent protocol which is quite good when dealing with large files.

Limewire uses Peer-to-Peer (P2P) networking, so basically you see what people have shared with you. When you seed with a Torrent manager such as Azureus it is similar to sharing with p2p, but there is a difference that make torrents MUCH better:

Depending on the torrent site (or tracker as its known) you choose to download a torrent from, (that is where you found it, since technically you download from peers) , the torrents are usually moderated so you are not downloading some nonsense with the wrong name and/or that is not infected with malware, like viruses, that most computer illiterates have in there computer. If someone does seed nonsense, they risk getting banned  from the torrent site (if its a good site that is). So basically what you choose to download becomes safer and more accurate.

I think Azureus is really cool, with µTorrent's features and more, but if you want to use it, prepare for some serious resource demands like with Limewire. It uses about 53MB of RAM on average. So far, from what I see from Limewire and Azureus, I'm inclined to think, Java-based clients are demanding on systems. Any comments to this assumption?