I am presenting one protestant view; I do not think there is a single protestant view.
I think it is correct, at a very high level; Buddhist thought looks at 'punishment' as less beneficial to persons than the Bible does. In practical terms it does not seem to have a big effect on government though for some more or less 'Buddhist' countries use capital punishment. Thailand and China are very good examples. Ignoring the practical aspect, the notion that pain and punishment should be resisted along with a high emphasis on passive kindness seems to be central to Buddhism.
I have always thought this is because the people who hold that religion have usually been without any power to resist the doctorial stance of their governments; they have developed a kind of spiritual 'coping mechanism' for the heartless cruelty of their societies.
The Biblical view on punishment is not a unanimously agreed one. I for example am more 'Buddhist' in my view of the Biblical term 'punishment'. I do not think God ever punishes His children, but those who are still under the curse of the Law, they are being punished and will be punished forever more if they do not accept that God punished their sins on Christ.
So the Buddhist view does not like punishment, but can't provide someone to take the punishment when it is finally necessary. The Christian view holds Christ as 'the punished One', meaning all believers will go unpunished.
It is difficult to compare religions because they start with fundamental positions that are in opposition. I am not aware that any other religion believes in ‘original sin’, which is a founding doctrine for Christianity. Christianity is also the only religion with grace (that is someone being totally punished for another, who receives no punishment on this account).
When it comes to how punishments are administered by the government for crime, or from parents with rebellious children, the New Testament seems to leave it to those authorities. However, cruelty is never tolerated in the Bible.
There is some ‘natural wisdom’ (as opposed to spiritual wisdom) in all religions. Therefore, it is not surprising that some verses from Proverbs seem to be just like Buddhist sayings. For example:
Those who are kind benefit themselves,
but the cruel bring ruin on themselves. (Proverbs 11:17)
The righteous care for the needs of their animals,
but the kindest acts of the wicked are cruel. (Proverbs 12:10)
The idea of punishment must be clearly separated between desiring to punish someone personally and civil laws to protect people. Desiring to punish is a sin, and excessive punishments indicates that desire.
The Buddhist would love the words of our Lord. For example:
38 “You have heard that it was said, ‘Eye for eye, and tooth for tooth.
’ 39 But I tell you, do not resist an evil person. If anyone slaps you
on the right cheek, turn to them the other cheek also. 40 And if anyone
wants to sue you and take your shirt, hand over your coat as well. 41
If anyone forces you to go one mile, go with them two miles. 42 Give to
the one who asks you, and do not turn away from the one who wants to
borrow from you. (Matthew 5:38-42)
Jesus as very strict against the desire to harm your brother, even calling your brother a fool in anger was putting you in 'danger of hell"
21 “You have heard that it was said to the people long ago, ‘You shall
not murder, and anyone who murders will be subject to judgment. ’ 22
But I tell you that anyone who is angry with a brother or sister will
be subject to judgment. Again, anyone who says to a brother or sister,
‘Raca,’ is answerable to the court. And anyone who says, ‘You fool! ’
will be in danger of the fire of hell. (Matthew 5:21-23)
In the end I think Biblical Christianity is more humane than all other religions because not only does it hold the ideal of kindness but it actually produces kindness in the heart by faith in Christ. Other religions can’t draw from the love of God in Christ as that is rejected. The fact that many under the name Christian have been very cruel only indicates that they might not have truly believed in the gospel:
Anyone who claims to be in the light but hates a brother or sister is
still in the darkness. (1 John 2:9)
For an in-depth understanding how punishment is different under Law verses under grace, see this post, for punishment and guilt go hand in hand.