One of my sons is married to an Italian, and the other to a Mauritian, so I have some sort of involvement in the difference between the two. (In fact, she and three relatives who are visiting the UK will be here in about an hour.)

The costs of being a legal immigrant from outside the EU are several thousands of pounds per year. I do not think it likely the EU will accept that readily for their citizens. So it seems inevitable that there will be continuing differences between the two.

There is also an argument to be made that one of the drivers of illegal immigration is the high cost of being a legal immigrant.