The theme of a young child taking on the world works brilliantly for the original TLoZ and again was put to compelling use in Ocarina (his youngest appearance to date). That theme of a mere child taking on such a perilous endeavor and through his courage alone being capable enough to prevail is pretty awesome.
This theme loses its effect when Link is older. When he's a teen it's simply boring because teens are boneheaded and have no sense of fear (along with crippling insecurities and an intense desire to prove themselves) so teen Link is pretty much courageous by default. Even so there is really nothing to be said for a teenager taking on such a perilous adventure. Granted, teen boys made up the majority of valiant heroes in most bloody conflicts throughout history, but that's mostly by virtue of them being able bodied. Still doesn't diminish their courage especially when they took to task willingly, but for as laudable and remarkable as that is it does come off as pretty standard.
An older young adult Link is arguably more capable. The oldest he's been is in Twilight Princess where he was already an accomplished rider, bowman and swordsman. Courage can come easier to adults, many of whom have developed the capacity to run headlong into danger knowing full well the risks. But when you've already had time to develop mad skills the confidence that provides diminishes the courage it takes a little.
I still find adult Link preferable to young Link but for no other reason than because I'm older really. The problem with child protagonists is that children and adults can have a difficult time relating to them. Children desire to roleplay as adults. They want to fantasize about how cool life will be when they're older. Adults on the other hand have difficulties shirking their adult sensibilities to relate to children. So adult heroes will appeal more readily to both children and adults.