Every bird is an individual and not all fit their species' norms. I'd stay open to the thought of several species and let a bird choose you, if possible. But with that said, I've heard screaming suns and its like nothing else I've ever heard. It made my ears ring after only two or three screeches. My green cheek's screaming is much more tolerable, but everyone has their preferences. Suns are beautiful, but their screaming is another story

You could look up suns and green cheeks screaming on Youtube and get an idea of what you'd be getting yourself into with either kind, if you haven't already.
My green cheek isn't nippy whatsoever. He's extremely affectionate and cuddly, and has never truly bitten anyone. The only time he nips is when the person on the receiving end deserves it, like my partner being thick headed and not listening when I say "Don't do such and such, Peeko doesn't like it". Peeko has been exposed to many children of varying ages ever since I've had him, the youngest being 3, and he's been an angel with all of them. Of course, they were well behaved and listened well when we told them how to handle him, which can make all the difference. I've been sure to get Peeko well socialized with people of different ages, genders, and races and he's never met someone he hasn't liked. He's bonded to me and would rather be with me, but he's still very willing to socialize and play with other people. Of course, with everything said, he's an individual like every other bird and that's not to say another green cheek would be exactly like him if you got one.
Since you have young(ish) children, I would see if its possible to get a conure that's been around children before with positive experiences because its never fun for anyone involved when a kid gets bit, then reacts by flinging or flailing and the bird literally goes flying :c
Overall, I would recommend a green cheek over a sun, but in the end you should go with the bird that chooses you and your family. Peeko chose me, and he's easily the best pet I've ever had <3