As you know, the word "similarity" can be both countable and uncountable. Based on this matter and whereas you can easily find some results for each case surfing the net, I have no idea surfing the net, which sentence bellow sounds more idiomatic and natural. I am wondering which sentence is correct:
1- They are like apples and oranges; there is no similarity between their personalities.
2- They are like apples and oranges; there are no similarities between their personalities.
Logically, #2 should be more idiomatic to me.