Compare data between 2 different schemas

We refactored our old database (some tables was dropped, some tables was splitted into 2 new tables etc). So now we have absolutely new DB schema which has many differences from old one. Some guy also has wrote application which migrates data from old database to new one.

I'm looking for methods/techniques to compare correctness of data migration. Is there any standard or often-used ways to accomplish such compare?

After some research, I found one technique how to do it, but I'm interesting in other ways: - Creating a VIEW of each table of the old database. I.e. I will try to represent in VIEW data in format of old table (old schema). And then compare data in old table with data in VIEW.

Thanks