"Like night and day" means "very different".
A. Where're ya from?
B. New York.
A. Ya like Tokyo?
B. It's OK--too crowded, rushed... noisy?
A. New Yorkers are used to it!
B. I'm from Long Island.
A. But Tokyo and New York are similar.
B. Like night 'n day.
A. ?
B. We don't run into each other. We have more space; it's quiet.
日本語訳
Like night and day は「昼と夜ほど違う」、つまり「まったく違う」という意味です。A「どこ出身？」B「ニューヨーク」。A「東京は好き？」B「悪くないけど、人が多くてせわしなく、騒がしいかな」。A「ニューヨークの人なら慣れているでしょう」。B「ロングアイランド出身なの」。A「でも東京とニューヨークは似ているよ」。B「昼と夜くらい違うわ」。A「え？」B「向こうでは人とぶつかることも少なく、もっと広くて静かなの」。
Here, speaker B is expressing an opposite opinion. She probably likes Japan--and Tokyo too--for their own qualities... but like many Americans--and especially New Yorkers--she feels it is best to share her true feelings: She doesn't think Tokyo and New York are similar (at least in the ways she explains that they are different)--in her opinion. And in her use of the expression, like night and day, she is perhaps being a bit sarcastic (saying the opposite thing-with other words), rather than directly contradicting speaker A and saying "no they are not similar". The complete unspoken--or suggested comment--would be: "Yes, they are similar--like night and day are similar," meaning "night and day are similar because they are parts of the day, but one is dark and one is light--so they are not similar at all!"
解答・解説の日本語訳
B は二つの都市が似ているという A の意見に反対しています。東京や日本を嫌っているわけではなく、それぞれの特徴を認めつつ、自分の感じた違いを率直に述べています。「昼と夜くらい似ている」という含みで、直接否定せず少し皮肉を込めた言い方にもなっています。