The main advantage with IIS7's integrated mode seems to be native .NET integration into the HTTP request/response pipeline.
Native integration gives you access to each and every request, even for static files, and requires no configuration on the server itself just a setting in the configuration file, something which makes shared hosting easier.
In IIS6 it was possible to integrate .NET into the pipeline by using a wildcard mapping (*) which basically gave you most of the advantages of IIS7 Integrated Mode, even though it's been said that wildcard mapping degrades performance, no one seemed to have specific numbers and this SO question actually shows that performance is not impacted at all.
I don't think it's worth the effort to change your code just to support Integrated Mode, stick to Classic Mode and turn on wildcard mapping if necessary.