I've worked on a few migration projects and a key part has always been data reconciliation.
I can only talk about the approaches we took, based on constraints around tools available and minimising downtime, and constraints of available space.
In all cases I took to writing scripts that worked on two levels - summary view and "deep dive". We couldn't find any tools readily available that did what we wanted in a timely enough manner. In fact even the migration tools we found had limitations (datapump, sqlloader, golden gate, etc) and hand coded scripts to handle the bits that we found to be lacking or too slow in the standard tools.
The summary view varied from project to project. It was part functional based (do the accounting figures for transactions match) for the users to verify, and part technical. For smaller tables we could just write simple reports and the diff was straight forward.
For larger tables we wrote technical reports that looked at bands of data (e.g group the PK into 1000s) collect all the column data and produce checksum, generating a report for each table like:
PK ID Range Start Checksum
----------------- -----------
100000 22773377829
200000 38938938282
.
.
Corresponding table pairs from each database were then were "diff"d against each other to highlight discrepancies. Any differences that were found could then be looked at in more detail.
The scripts were written in such a way to allow them to run in parallel looking at discrete bands. Te band ranges were tunable as well to get the best throughput. This obviously sped things up.
The scripts were shell scripts firing off sqlplus reports, and similar for the source database.
On one project there wasn't enough diskspace to do these reports, so I wrote a Java program that queried the two databases side by side, using block queues to fetch and compare rowsets. Being in memory meant this was super fast.
For the "deep dive" we looked at the details for key tables, or for tables that reports a checksum difference.
For the user reports, the users would specify what they wanted to see, and we wrote the reports accordingly.
On the last project, the only discrepancies found were caused by character set conversion issues (people names with accents weren't handled correctly).
On projects where the overall dataset was smaller we extracted the data to XML files and wrote a Java tool to processes pairs and report differences.