I love GMail's conversation view, but AFAIK, not really many other desktop email clients have adopted it. Who else has it?
In particular, it doesn't include you or your sent mail in the conversation (http://i.imgur.com/Atkcu.png). It only lets you expand the email quotation to let you dig through nested context (http://i.imgur.com/1Zj2e.png).
Compare this to gmail (http://i.imgur.com/mLel3.png) that actually handles it as a conversation. It's one of the reasons I use Mailplane (thin wrapper around gmail) instead of Mail.app.
I use gmail, and I use Outlook and PINE and Netscape Mail and Eudora etc and I can't work out what was improved.
Threads are a sort of pre-Web 2.0 way of doing things. The messages are linked together in the tree portion of the UI but are still viewed individually in the viewing pane. They aren't stacked together like they are in a typical conversation view.
Conversations are a more modern, succinct take on what threads were trying to be.
Also, if I receive a message, reply to it and archive that thread it goes away. But if that person reply's again it brings the whole conversation back to the inbox so I can see the previous messages as well.
As someone who uses the inbox as a partial todo list that is amazing. It makes it difficult to switch from gmail, although I've been using mu4e[1] inside emacs.