From a theoretical point of view how much do institutions matter?
Well it depends on who you talk to. As you have seen, neo-functionalism affords a large role to institutions in the integration process whereas intergovernmentalism (LI included) attributes, relatively speaking, a much smaller role to supranational institutions.
New institutionalists see institutions as very important. Indeed, new institutionalism sees institutions as central in determining what happens in EU affairs. For new institutionalists, institutions represent a key variable in the integration process as they can determine and affect the course of the EU policy.
We can identify three main types of new institutionalisms (rational, historical and sociological) and each of the three variants of new institutionalism sees institutions impacting on policy outcomes in different ways.
Click here to read about new institutionalism.