The Shield, but it's not fair to compare them.
New Day has been successful. No one expected the gimmick towork, but they're now probably the best tag team of this era.
However the Shield was simply better. They had excellent matches with the Wyatts, Evolution, and Ryback/Kane/Bryan. New Day has had some really good matches, but they don't compare.
Maybe a better argument is which group did more for its members? You definitely could argue the Shield, but I would argue New Day. Big E and Xavier were generic as possible, and now they're two of the most charismatic wrestlers on the roster. Kofi had a lot more success, but he wasn't doing much either. Don't get me wrong - the Shield definitely elevated Reigns, Ambrose, and Rollins. Where would they be without the group? Yeah they would have success but probably not as much.
So yes New Day is great, but the Shield was that much better.