I think that the Yankees should be more celebrated because they have a better record than the New York Giants. They have won and been in far more championship games and play-off games than the Giants have. The Giants have only won four Superbowl Games from 2010-1987. If you look at the Yankees records they have won 27 World Series Titles in 40 appearances.
The Giants have had more recent success than the Yankees but the Yankees have had the longest success and have been the best team in the league for all history. The Giants have won without huge names which has made them notable, but the Yankees have built dynasties throughout the years and with their bank roll it can only go up.
The question of celebration often relies on success. If the New York Giants had just won the Super Bowl, then they should be celebrated more than the Yankees who had not won the World Series that year. If the opposite were true, then the Yankees should be more celebrated for that year. Since neither have achieved this, the history of each franchise can be analyzed. The Yankees have clearly a more productive past than the Giants and have earned the right to be more celebrated.
I believe both the New York Giants and the New York Yankees are very important to the people of New York City, but neither should really be more celebrated than the other. Since they participate in two different sports I believe the citizens should support them both equally as they all benefit from their presence.
The New York Yankees should be more celebrated because they've won more titles and they play in America's game. The Yankees play more games per year. They have 27 World Series titles, the most of any baseball team. The Giants aren't even close to being the best NFL franchise in the history of the game.