To convince is to change the mind.   

So, the answer to the question 'Which is better, convict or convince?' is obvious.   

Our criminal justice system fails because it is only able to convict and punish criminals.   

In the same way the Law, under the Old Covenant, was only able to convict and punish.   

Those who would preach a message of conviction fall into the same futility of the penal system and the Old Covenant.   

The message of the Gospel (good news) is to attract people to God.   

The reality is that people who are not attracted to God by the Gospel cannot be saved.   

Those who seek forgiveness only to escape hell miss the fundamental purpose of creation.   

God created the heavens and the earth to raise up children unto Himself.   
Our purpose in existence is to come into intimate personal relationship with God.   

God is a Spirit and so He births us into the Spirit Realm by Grace Through Faith in the Gospel of Christ Jesus.   

The gift of God is Eternal Life.   It is the gift of Himself, the Holy Spirit.   

And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. - Joh 17:3

Eternal Life is a Gift.     That Gift is to be Born of the Holy Spirit as a New Spirit being and made One with God.      It is in the Holy Spirit and His Word that we Fellowship with God and come to Know Him.

A person who does not appreciate the gift of God won't receive it.   

A person who does not receive the gift of God abides in death.   

A person who does not appreciate this gift is not worthy of God.   

A person who does not appreciate and receive this gift will be destroyed in the Lake Of Fire.   

God cannot make a person appreciate Him.   Neither can we.   

Accordingly, our message to the lost is that today is the day of salvation offered by God to us by virtue of His own shed blood.   

The Holy Spirit will convince the person of the Truth because He is the Spirit Of Truth.   

It is their decision to receive the Truth or to reject it.