Which is essentially what a remake is - a re-release with quite a number of optimized features, a port would have been pretty much the same game with minor touch ups to it (See: Twilight Princess for the Wii or pretty much every portable Ridge Racer).
...There isn't really much to add since the whole point was to introduce the game to newer players who weren't around to play the original version. If you played it before, then you would generally find it to be lacking, would you not?
And I have HG as well, but on the same day of OoT.
And a better Master Quest mode, Boss Rush mode, integrated gyroscope controls that actually work...etc.
Four Swords Anniversary collection basically slapped on an hour long (or even less?) single player mode with the nifty, but somewhat inconvenient prospect of switching through Links. I would rather they had just included an online component with the experience as well.