Jersey City versus New York City

It might be a strange post that I am adding here, but we are in the process of maybe moving to USA. My husband will be working for the same company in an office located at Bloomfield.
My idea is to live in NY, probably Brooklyn, because of the "vibe" that hangs around NY...but Jersey City might be a better option when it comes to raising kids (we have 2 of 8 and Protected content commuting.
Can somebody help me further with nice neighbourhoods for kids, but still trendy enough for us parents? Who are close by to NYC?
Or are there people that lived in both places and can give a good comparaison....