Both sides of the conversation. Mail.app's thread feature only shows emails you have received, without weaving in the emails you have sent.

I'll just expand on what YooLi said.

You can see both sides of the conversation, and I prefer how a conversation is treated as a single entity. If I archive a conversation, all messages in that conversation are archived. And if a new reply to the conversation comes in, the entire conversation gets pushed back to my inbox.

Apple Mail's Organize by Thread feature is retarded. It considers any messages that have the same subject to be in the same thread. Gmail's Conversations identify the actual threads/conversations instead.