Oh boy, I was researching this heavily a while back.
You will NOT be able to synchronize the two systems, the way JIRA works with SVN. Atlassian thought about integrating with TFS, but actually dropped it from their priority list. There was a JIRA<->TFS migration tool over at Codeplex (don't want to look for it now), but it ceased working.
What one actually wants is to see the check-ins from TFS within JIRA (just like SVN) and that you can associate a JIRA bug ticket with changeset, so the customer can directly see when something will be deployed - and that... not possible. Another great thing would be to synchronize TFS work items with JIRA, so that JIRA is the outward facing bug tracking system and you can use TFS for internal task management... not possible
Here is the official thread on the Atlassian Forums: Integrate with Visual Studio Team Foundation Server (replacing VSS). Last official word (June 2010):
Based on customer demand, we are focusing on git and Mercurial support in the short term. We may revisit TFS support at a future date, but it is not currently planned.
On another Atlassian Front (Bamboo) you have the same picture:
TFS support is currently low on our priority list and unlikely to be implemented over the next 6 month. (from Support for Team Foundation Server)
The same goes the other way around - Microsoft integrating with Atlassian (sounds kind of naughty). I could find one official ticket here: JIRA TFS Integration. Last official word (December 2009):
Thanks for the feedback about Jira-TFS integration. We're tracking the request for an integrated solution on our feature backlog. We are also improving our Migration Tools platform to hopefully enable partners and customers to build integration solutions like this to meet their individual needs if we are not able to immediately provide such solutions.
I love JIRA, but I just hate that the two systems don't run together well. All you can do to synchronize your work items with JIRA is, you guessed it, manual labor.
PS: To answer your question about having the two run together: It does work. JIRA is great for customer contact, because it is "easy" to understand. TFS is great for your team (burn down charts, management overviews, code-centric).
Edit (2012):
Now there have been some improvements:
The Atlassian Connector doesn't include full integration, but at least you get to see all JIRA issues within Visual Studio and you can comment on stuff and search for stuff. So basically you are only missing code checkins. It is enough for most purposes - otherwise you have the other two commercial choices.