to make it simple, when you say 成为, "it 成为 something." It's not big change. It only gets better, worse, more beautiful, more, less, bigger, smaller, hotter, colder. (These are only examples) when you say 变成, "it 变成 something." It's usually big change. A frog 变成 a prince, but a frog never 成为 a prince. A woman 成为 my wife, but if a woman 变成 my wife. Then I mean, this woman can change her shape (a witch xD)

成为means growing up,from a low level to a high level. -He 成为 a qualified soldier after a series of rigorous training. 变成just be from one level to another level,likely to a lower or equal level. -It make us surprised that he 变成 such a rude man.

”成为“ means " change into something good or a good person" . ”变成“ can means "change completely in appearance and character / change into a bad person / something good have changed into somethng bad "

”成为“ 和 ”变成“ 的 difference are same as "transfer"and"trasform" ”成为”means “someone got a title 成为一个英雄 “or something people add to them ，because they have had influence on them。 ”变成“means change completely in appearance and character。

It's hard to tell the differeces between them. I think they do have slight differeces in use. Maybe I can give you some examples occured in my minds to help you figure out the slight differeces. I think when a person becomes some charactor, it'll be better to use "成为“ rather than "变成”. For example, 他最终成为了国家主席/总统。我们成为了朋友。 And when you say something or person changes into something especially in form, I think "变成“ will be better. For example, 蝌蚪长大，变成了青蛙。月圆之夜，他变成了狼人。擎天柱变成了汽车，紧追敌人。 So, these are some examples.Maybe some others could add more.