Unfortunately I no direct experience of either ! The kitchen that serves the princess grill on QE2 also serves the Caronia restaurant. The Queens grill on QE2 has its own kitchen. On QM2 I think a dedicated kitchen serves both the Queens and Princess grills but I am not certain.
The Princess grill on QE2 was built as the original first class dining room before the Casino was turned into the Queens grill and balcony cabins added.
I think the Princess grill is the classiest of them all, it also has a semi private cocktail bar which connects via a spiral staircase to the restaurant.
I think the Queens grill is for the Nouveau Rich which unfortunately I'm not, I have also heard it called God's waiting room !!!