It is possible to synchronize your mobile device with Outlook if it is installed on a different computer (without Thunderbird/Sunbird being synchronized on this machine). So you can synchronize your mobile device with Outlook and Thunderbird if they are installed on 2 different machines. Simply be aware that all the modifications performed on either computer will be replicated on the other one. Don't forget to regularly backup your data, especially if it is the first time you synchronize with this configuration.
On the machine where you synchronize with Outlook, select "contacts, calendar, tasks or E-mails" in ActiveSync/Windows Mobile Device Center options. On the machine where you synchronize with Thunderbird/Sunbird, select "Contacts, Events, Tasks or Mails" in BirdieSync/Activation.