I guess you mean the two clients that are found on /alfresco and /share respectively?
/alfresco houses the original client, known as Alfresco Explorer. It's designed to give full control of the Alfresco repository and provides features such as advanced search, extensive scripting possibilities, workflow control, content rule management etc. However, it's not very end user friendly.
/share houses the Share client, which is more lightweight and obviously designed with MS Sharepoint in mind. It lacks the extensive control of the Explorer client, but it has some other collaboration features, such as wiki, blog, discussion forum and the possibility to invite external users to some or all of the content. It's also designed to be more easily extendable than the Explorer client, since it's very much based on javascript.
Which one is preferable over the other very much depends on what you want to do. It is said that the Share client will become more powerful in coming versions, but today you more or less need to use the Explorer client to administer Alfresco in a good way. However, end users could very well do with the Share client if they only need basic functionality.
