Both are important--work and what they are supposed to work for.
Their work is to believe. Believe--how hard is that? Believe--is it possible? Believe--does he mean creed or something else?
The goal is bread. And they want it. They ask how they can get this true bread from heaven. Jesus says, "You've already got it. I am the bread of life."
This passage is raising a lot of uncomfortable questions for me today: Why do I go to church? What do I pray about? What am I working for? How do I know if I have passed the "believe" requirement. Am I looking for a sign? And most disturbing, what do I do with verse 35? I know that hunger and thirst exist, and I know that good, believing people are among the hungry and thirsty. And I know that I don't want to metaphorize the terms completely.