The title of this thread falsely pits one chapter against another. But that is not how they should be understood. They are both referring to the same person -- the sinner saved by grace.
In chapter 7 Paul shows us that even though he is an outstanding apostle, his "flesh" (the sin nature) has not been eradicated: For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not. (v 18)
This verse also tells us that the flesh cannot perform that which is good, since there is nothing good in the sin nature (inherited from Adam). And what is true for Paul is true for all believers. The flesh is still there, but needs to be crucified.
But in chapter 8, Paul shows us that the flesh cannot, and must not, dominate the believer, because of the power of the indwelling Holy Spirit to overcome sinful tendencies: But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. And if Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness. (vv 9-10)