I agree with doug. "虎父无犬子“is a commendatory term. and "Like father like son" is more neutral or just like doug said, it describe defects of character. So, I dont think they're the same. Maybe 有其父必有其子 is closer to "like father like son"?

in US, this phrase is mostly used to describe different generations acting in a similar manner. Mainly used to describe defects of character.

Yes , it is the equivalent proverb to the Chinese one : 虎父無犬子 "Father a lion, son cannot be a dog " In both cases it is an expression of respect and honor,although both are expressed in different ways. With the position of honor the father holds, the son can't be in a lesser position or the son is as much as respected and recognized as his father is.

I misread the question and don't know how to delete the comment--sorry!