You'll want to use client side code like the Client Side API or Web Services for connecting to SharePoint just like silverlight.
XBAP is only for IE/Firefox
XBAP requires the correct version of .net preinstalled
XBAP must be installed onto client computer
Can run full trust
**XBAP is installed on first access and re-installed/updated if the XBAP changes similiar to ClickOnce deployments.
Silverlight is cross platform and supports more browsers
Requires small browser plug in and will re-direct user to install required components.
**Silverlight Client installation is a lightweight version of the .net framework, so as long as the client is installed the version of .net doesn't matter.
If you are working in a controlled environment and know the .net version installed on clients than XBAP gives you more options.
If your base is diverse OS (Windows, OSX, Linux) or Browsers (IE, FireFox, Chrome, Safari) or you can't guarantee they have the correct .Net version installed I would go with Silverlight.
There are a number of dicussions posted on StackOverflow as well (just a couple)