If it is white box and very technical then the approach may be quite complex. If you are looking at the black box system level ie the same post migration this is a slightly less complex requirement to test, though still potentially a large task.
Normally in any migration the minimal criteria to lok for is no negative changes to be identified on performance, functionality and data integrity.
This can be done by using the same sort of story based end to end test on both systems prior to the final implementation on hardware that is scaled in the same proportions to live.
I work at the white box level and so also look to review the architectutal design models, the data flow and types of communication used, I also have a tendancy to look for locks and contentions on the system and bottle necks as they may be introduced if we need to change the internal logic of the applications.
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