It is true that NPs are trained to be independent and in most states they are. It is also true that in some states PAs are working independently in rural clinics.
As far as the pay goes, that is always negotiable. I have always been in the top 1% of income, last year I made 180k
I make more than all the PAs I work with and have at every job I have had. It depends on your negotiating skills.
Lastly, the highest paying group of PAs or NPs are CRNAs. They make muchore than PAs.
The bottom line us this, money is out there and can be made by anyone. But if it is idependence you are looking for, it is easier to be independent as an NP. The laws are written that way in most states. Sure you you can practice in 3rd world countries, so can nurses and PAs, and do way more than you were trained for in school.