You want to compare the Registry on two hosts or compare the Registry on the same host after you've installed an application or made other modifications to the Registry.
Using a graphical user interface
When you export the Registry, you are simply exporting the contents of the Registry to a text-based file, which you can use to compare against other export files. Windiff is just one example tool that can compare text files and show the differences. Some text editors can do the same (e.g., Textpad is a favorite of mine).
If you only want to see the changes that an application makes during installation, another option is to use the Sysinternals Registry Monitor tool. You can configure Registry Monitor to display only write events for a certain key. For more information on Registry Monitor, see Recipe 9.12.
MS KB 171780, "How to Use WinDiff to Compare Registry Files"