There are few changes to code, most important ones are search forms for header, forum and topic. Form posting method changes to "get" (optional, form will work with "post" too) and hidden parameters are handled differently. The rest of changes are bug fixes that aren't important.
Download phpBB 3.0.8 and 3.0.9, compare files to see full list of changes. There are many tools that can do it. I recommend FileMerge for Mac and WinMerge for Windows.