The procedure should be identical for either, I think. I use Outlook Express, but I have a bit of experience with Outlook.
I think you have to go to File>Import and Export or something like that. For your contacts, you can either export as comma-separated-values or as an Outlook data file. You shoudl be able to to export your messages as a data file or something similar.
Alternatively, you could just find the data files for Outlook (they're somewhere in the hidden Local Settings folder on C
and copy them onto the new computer.