What is more important, close reading or big ideas?

It's important to remember that we generally use close reading to facilitate wider discussion about texts, not as an 'end in itself', so it is important to have a combination of both in your essays. The exciting thing about English Literature is that all parts of the text often interact with each other, so that features of style and structure can reinforce prevalent ideas. For example, if you were close reading an Emily Dickinson poem, you might suggest that the riddle-like structure of poems like 'This World is Not Conclusion' is notable because it compliments Dickinson's 'big ideas' about ambiguity.Therefore, you should use a combination of close reading and big ideas, allowing the two to work together, rather than forcing them to compete.