Kirby
Not a fan of either, particularly. I voted Paper Boy over Zelda because I love that game... but since I don't care about Kirby's Dreamland, I'll vote for what is generally regarded the better game and vote for Zelda.

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There is a reason this game is on most top 5 lists of all time period (not just nintendo).
Ocarina all day every day.
Zelda wins 4-1.

Thanks Taker_2004 for the banner!
Welcome to the Greatest Nintendo Game of All Time contest's second round!
I will put the matches up every other day, and each round will be open for three days (so there'll probably be 2 or 3 matches taking place at any one time).
ROUND TWO, MATCH ONE
Kirby's Dreamland (GBC)
Round 1: defeated Pokemon X & Y
Kirby's Dream Land is a 1992 action-platform video game for the Game Boy, developed by HAL Laboratory and published by Nintendo. It is both the first video game in the Kirby series and the debut of Kirby himself. Being the inaugural Kirby title, it created many conventions that would appear in later games in the series, including Kirby's basic moves. However, Kirby's trademark "copy" ability would not appear until Kirby's Adventure, released less than one year later. Kirby's Dream Land was designed by Masahiro Sakurai, who intended it to be a simple game that could be easy to pick up and play even by those unfamiliar with action games. He offered additional optional challenges for more advanced gamers such as an unlockable hard mode and the ability to edit Kirby's maximum HP and starting number of lives. Kirby's Dream Land was re-released on the Nintendo 3DS via the Virtual Console in 2011 and was also one of the games included in the compilation game Kirby's Dream Collection for the Wii, released to celebrate Kirby's 20th anniversary.
The Legend of Zelda: Ocarina of Time (N64)
Round 1: defeated Paper Boy
The Legend of Zelda: Ocarina of Time[a] is an action-adventure video game developed and published by Nintendo for the Nintendo 64. It was released in Japan and North America in November 1998, and in Europe and Australia in December 1998. Originally developed for the 64DD peripheral, the game was instead released on a 256-megabit (32-megabyte) cartridge, the largest-capacity cartridge Nintendo produced at that time. Ocarina of Time is the fifth game in the The Legend of Zelda series, and the first with 3D graphics. It was followed by a direct sequel, The Legend of Zelda: Majora's Mask, in 2000.
WHO WINS? YOU DECIDE.
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