The views are similar, but the courses are actually quite different design-wise.
Both are incredibly scenic with ocean views, views off property to the surrounding hills, etc.
Mid-Ocean has the history advantage, as the course originates with CB MacDonald and Seth Raynor, and contains the roster of template holes. It is a Golden Age design in all aspects with push-up greens and strategic bunkers. Yes, it is expensive, but incredibly memorable. You will not be disappointed.
Port Royal is modern through and through, an RTJ course dating to the 70s. It was recently refurbished and strengthened, and it is a very difficult test of golf. Greens are elevated, bunkers are deep, and the greens fee still is not low. No one hole at Mid-Ocean is as scenic as #16 at PR, an all-or-nothing par three on the cliffs, but M-O would win a hole-by-hole match play handily.
If given 10 plays, I would probably go 8-2 in favor of Mid-Ocean, and that might be generous.