Neutralizing antibodies against influenza have generally been classified according to their recognition sites, with antibodies against the head domain of hemagglutinin thought to inhibit attachment and antibodies against the stalk region thought to inhibit fusion. Here, we report the development of a microfluidic assay to measure neutralization of viral entry that can clearly differentiate between effects on attachment and fusion. Testing multiple broadly neutralizing antibodies against the hemagglutinin stalk domain, we obtain a surprising result: some broadly neutralizing antibodies inhibit fusion only, while others inhibit both fusion and viral attachment. Antibodies binding the globular head domain primarily inhibit attachment but can also reduce the fusogenic capability of viral particles that nonetheless bind the receptor. These findings shed light on the unexpectedly heterogeneous mechanisms of antibody neutralization even within similar recognition sites. The assay we have developed also provides a tool to optimize vaccine design by permitting assessment of the elicited antibody response with greater mechanistic resolution.