Data integration is the process of standardising the data definitions and data structures of multiple data sources by using a common schema thereby providing a
unified view of the data for enterprise-level planning and decision making.
on the other hand, Data Migration is the process of transferring data between storage types, formats, or computer systems.
This process is most often required when organizations upgrade to new systems or change computer systems.
Dynamics CRM implementations often need to choose between this choice since CRM is all about Data.
A correct design time decision can often help reduce the complexity of design and cost of effort and implementation.
For eg, if one of the main focus of customer requirements is to centralize storage of Data, it is always better to think whether the business requirement is to have centralize storage or to have view
that there is centralized storage.
In terms of choice, If its just view of data to be looking centralized it is Data integration for CRM, else it is Data migration from heterogeneous sources to CRM.
This is just one business case to explain the choice.
I will continue to pen more on this in the coming days and weeks. Happy CRMing!
Note: Definitions for the terms were binged!
MSDYNAMICSBLOG BY DEEPESH 
If it all possible I prefer integration over migration especially in scenarios that involve larger data sets or data that has a correlation dependencies. Sales revenue for example is always a touchy topic because typically CRM is not the system of record for this data and there can be many variables where sales can be misrepresented. On the other hand the political/implementation environment may force a decision one way or another despite it being against your better judgment and you have to make due with what you are given.
Totally agree to your point of view, in middle of the same story myself right now 🙂