"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.

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!"