It would entirely depend on which game it is. Ocarina of Time would be much easier to do a minimalist run of, as to complete it 100%, there is a large amount of items and Golden Skulltulas to collect throughout the game, although, if you had more patience that I do, it would be probably be easier to beat the game 100% as you'd actually be able to spend the time looking for Skulltulas that you've missed in temples...etc, something which I can really not be bothered to do, unless I knew where everything was and could easily collect it along the way of course.
Twilight Princess is a game that's extremely easily to beat on a minimalist run, as I have done it before, and I found it easier to complete than the 100% run I made. Once again though, that's because I am not patient enough to go back and collect any thing that I have missed, such as Poe Souls, from within a temple. Although, once again, if I knew where everything was, it would be just as easy to do either, but I do not have such extensive knowledge of the game, or Ocarina of Time for that matter.
Going back to an oldest Zelda of all, I'd definately find it much easier to do a 100% run through than a minimalist run, as I always take a lot of damage whilst in the dungeons, or even in the overworld, particulary the north-east area. I don't really have extensive knowledge of Legend of Zelda though, so I'd imagine that I'd either give up or find it extremely difficult to find everything that I could possibly collect in that game.
Finally, for the hand helds, I found Phantom Hourglass rather easy to complete, and I imagine that Spirit Tracks is the same, so I'd find it easier to do a minimalist run. Especially considering there are so many pieces that you can collect to customise your boat with in Phantom Hourglass, and that to find them all, it is a rather random process, something that would probably take many hours to do, even with a fair amount of luck.
For me, it wouldn't matter if I was playing through the game for the first time or not for any of the things I have said above, so they'd stay the same even if I was testing the games out to see whether a minimalist or a 100% run was harder.