The original LoZ is fine just as it is. It's pretty much the dream Legend of Zelda title that couldn't be expanded upon to make it any better, so that means it should remain as it is and not be converted into something else, such as a 3-Dimensional game. Personally, I found nothing wrong with the controls; they were fine on the NES and Gamecube controllers, the latter of which went with the Zelda Special Edition disc.
On the other hand, the Adventure of Link could use a revamp in some aspects, IMO. My top preference would definitely be altering the sidescrolling perspective to an overhead view to make it less Mario and more Zelda. Next cut down on the difficulty so that casual players such as myself would be able to enjoy it as well. You don't really need hundreds of Tinsuit soldiers charging at you in the first Temple; just a large group of them in a single screen unit would be fine. In that screen unit they could charge at you, and it would be you who had to either evade and side-attack the enemy, or slash out with your sword before taking a blow. Thirdly, make a real overworld. I have no idea what they were thinking by creating a field where you had to dodge enemies rather than fighting them. But I'd want them to make an overworld just like the Zelda 1's or A Link to the Past's. Just don't go back to that. And lastly, fix the save system. No need to return to the starting spot after saving and turning he game off or dying.