The 2nd one looks like the settings for Outlook Express, not Outlook. If you haven't set Outlook as the default Mail client, that would fix it. Open Outlook directly and configure a mail account. If you are positive that you have Outlook as the default mail client on the 2nd machine then you probably don't have it configured for Corporate or Workgroup. I don't remember where you change that in the program though. It is under Tools -> Options -> Mail Services tab -> Reconfigure Mail Support button, when you have it set for corporate/workgroup already, but I don't think the the Mail services tab exists if it is set for Internet Only. It might be under the Tools -> Options -> General Tab -> Advanced Settings for E-Mail. I can check on that later and edit the info into this post.
Edit I checked and the issue is that the Outlook is set to Internet Only for e-mail. You need to change that to Corporate or Workgroup. The option in Outlook is under Tools -> Options -> Mail Delivery Tab -> Reconfigure Mail Support Button. Go through the Wizard and choose Corporate/Workgroup. You can still set up POP and IMAP accounts this way, and you can also connect via MAPI (Exchange) as well. It has all the Address book options and that you want as well.