It is true that we are both, except that one is in the past tense. We were sinners, now we are saints. When you read the gospels, you see the apostles constantly using positive statements about our identity in Christ. We are saints, we are the redeemed, reconciled to God who worship in the beauty of holiness. Today, I hear more about how we are all washed up. "I am just a sinner saved by grace, etc" Now don't think that is me looking down my nose at anyone. I can completely relate to needing the mercy of God at all times. It isn't how the bible tells us to think about ourselves, however.
Now, it's true that the apostle Paul called himself the chief of sinners, but he also told us why he said that; because he persecuted Gods church. Clearly, he wasn't doing that at the time he wrote that. The way that we think about ourselves will determine a lot in our walk with the Lord. If we think of ourselves as defeated then we will be (as a man thinks in his heart so he is), but if we stand upon what God says: that we are called of God, righteous because of Christs blood, and having authority over serpents and scorpions, then we will be that with the mercy and grace of Jesus Christ.