Why do electron-rich aryl groups have greater migratory aptitudes?
The answer varies slightly depending on whether the migration is one-step or two-step via an intermediate.
In either case, the respective transition state or intermediate looks like this:

You can see that the middle structure would be stabilized most by a group that is able to stabilize the ring via resonance, for example, an alkoxy substituent.
If the mechanism is single-step, then that substitution would stabilize the transition state and make this migration the fastest.
If the mechanism is two-step, then we can invoke the Hammond postulate to say that the transition state leading to the higher energy intermediate will resemble it in structure and thus also be stabilized by the same kind of substitution, leading to the same conclusion.
We therefore suggest that the propensity of migration is X=OMe &gt; X=H &gt; X=NO₂.