No. Christians have been set free from the reign of sin. Does that make us sinless? Not necessarily, because we are still flesh. However, now if we sin we have a mediator between us and God - the man Christ Jesus.
We also have the ability to walk in the Spirit. If we walk in the Spirit, we will not fulfill the lusts of the flesh. We have also been set free from the curse of sin. Non-believers do not have the ability to walk in the Spirit, are ruled by the lusts of the flesh, and are subject to the curse of sin and are bound servants to sin.
While Christians are not perfect and sinless, we have a means by which we can crucify our flesh and minimize the influence of sin in our lives through prayer, submission to God, and to HIS word. We do not have to be servants of sin, or ruled by sin. When we do mess up, we do not face condemnation and have an advocate. Non-believers do not have this hope. They are servants to sin, bound by sin, and have no advocate to plead their case when they stand in judgement.
You are better now than when you were bound by sin, you said. But you won't say that you are better than other people who are still bound by sin. Why not?
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Hebrews 13:23 Know ye that our brother Timothy is set at liberty