It's ideal to have the CRM's highest user permission level in order to access all of your data.
In some cases, the user privileges in your target CRM regarding creating, owning, and object inclusion are more limited than your source CRM user privileges.
As an example, say user privileges in your source CRM include deal creation, but in your target CRM, deal creation is excluded. This would result in the deals created by users in your source CRM not being migrated to your target CRM.
To avoid this issue, make sure that your user privileges in both your source and target CRMs correspond before migration, and that your users have full permission with regards to access, creation, and object record ownership.