Savings vs. Debt

Should I start an emergency fund or pay down some credit card debt? This is something I keep going back and forth about. I closed a checking account at US bank today because I recently got married and are combining our accounts at WAMU. They have free checking and a way better savings rate (as of this post the rate is now 5%). I have about $6k in credit card debt and am bringing over about $600. Do I use that $600 to start an emergency fund, or do I pay off part of the debt? At 5% interest I'll make about $30 in interest on the $600but pay considerably more in interest on the debt over the year. I like the idea of having an emergency fund in case something happens, but is the comfort in knowing that money is there worth holding my credit card debt a little longer??? 

Have any thoughts?