The main different is that the integrated mode actually make IIS and asp.net work as one, each request pass from "an ordered list of events".
In classic mode (not integrated), the IIS is first processing the call, then send it to asp.net for "second" processing.
The integrated is faster and lighter because you have less call, less steps, inside IIS.
Also note that on integrated mode the Request is not available on Application starts, on global.asax
You can read more details at: http://www.iis.net/learn/get-started/introduction-to-iis/introduction-to-iis-architecture