If you ask me I do not think raising children is as simple as choosing between punishment and rewards, Personally I believe that punishment and rewards both have their place, They have to be used wisely,Leaning much to one side can create problems of its own.
Growing up many of us were disciplined whenever we did something. Sometimes it was a scolding sometimes it was a punishment,Depending on the home it could even be a spanking, While I know not everyone agrees with that approach today I still think that discipline is a part of raising a child, That said, I also do not believe that every mistake should be met with punishment.
Children are still learning, They are going to make mistakes because that is part of growing up, If all they ever receive is punishment they may become fearful of actually understanding why what they did was wrong, they might avoid getting caught than learning the lesson behind their actions.
On the hand rewards can be a great way to encourage good behaviour, when a child is praised for being honest, hardworking or kind it gives them confidence and encourages them to keep doing those things, It does not always have to be money or very expensive gifts, sometimes a simple hug or allowing them a little extra playtime can mean a lot to a child.
Those little moments stay with them.. Here is where I think people also have to be careful...... If a child starts expecting a reward for every good thing they do that can become another problem.
Imagine a child saying, What will you give me if I wash the plates? Will you buy me something if I pass my exams? At that point they are no longer doing the thing because it is right they are doing it because they are expecting payment for it, so I do not think that is the lesson we should be teaching.
That is why I feel that balance is the approach, good behaviour should be Appreciated, while bad behaviour should have reasonable consequences, not harsh punishments that leave scars but consequences that help the child understand why their actions were wrong,
I also think that communication is something many parents overlook, Sometimes instead of immediately punishing a child it is worth asking why they behaved the way they did, maybe they were angry maybe they were influenced by friends, maybe they simply did not know better, understanding the reason behind the behaviour can help parents respond effectively.

Every child is different too, what works for one child may not work for another, Some children respond well to encouragement while others need boundaries, that is why parenting does not come with one formula, at the end of the day the goal is not to raise children who are only afraid of punishment or constantly chasing rewards, the goal is to raise children who understand wrong and choose to do the right thing even when nobody is watching,
For me that is what good parenting is, about, so if I had to choose I would not completely remove either punishment or rewards, I will use both punishment and rewards, with wisdom, patience and plenty of love,because children do not just need discipline they also need encouragement.