Welcome to the group. I'm new here myself.
Do those verses show that the Christian is more able to fulfill God's commands than the old testament believer was? No, they do not, but maybe not in the way you might initially think.
Jer 31:33 and Ezek 36:26 are both in the OT, and indicate that they are the only way to fulfill God's commands. Your question assumes that the moral law could be fulfilled in the OT in a different way than in the NT. That's not the case at all.
Paul goes into some detail on this point.
knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified. Galatians 2:16
Note here that no flesh shall be justified by the works of the law. There is no distinction between OT and NT, Jew or Gentile. In short, it is impossible to be justified by anything other than faith in Christ.
For as many as are of the works of the law are under the curse; for it is written, “Cursed is everyone who does not continue in all things which are written in the book of the law, to do them.” Galatians 3:10
If one chooses the path of the works of the law, the only way to avoid a curse is to keep them all, all the time. But faith in Christ is the only viable option because nobody, OT or NT, Jew or Gentile, has kept the law perfectly. Paul spends a big chunk of Romans explaining this.
For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law Romans 2:12
for all have sinned and fall short of the glory of God, Romans 3:23
Whether without the law or in the law, we are judged and destined to perish because all of us have sinned and fall short.
What then shall we say that Abraham our father has found according to the flesh? For if Abraham was justified by works, he has something to boast about, but not before God. For what does the Scripture say? “Abraham believed God, and it was accounted to him for righteousness.” Romans 4:1-3
For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith. Romans 4:13
Here Paul points out that the promise was given to Abraham through faith, not the law. Right at the source of the chosen people, the path to righteousness has been faith.
Therefore, if an uncircumcised man keeps the righteous requirements of the law, will not his uncircumcision be counted as circumcision? And will not the physically uncircumcised, if he fulfills the law, judge you who, even with your written code and circumcision, are a transgressor of the law? For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God. Romans 2:26-29
So here we find Paul's encapsulation of what true conversion is, for both Jew and Gentile. To be truly one of God's chosen people, a true Jew so to speak, one must be a Jew inwardly. Circumcision of the flesh has no moral worth in itself because circumcision of the heart is and has always been what truly counts. So also, outward compliance with the law, in whatever imperfect form it may take (see Isaiah 64:6), has no moral worth in itself because inward compliance with the law is and has always been what truly counts.
A believer in the OT could fulfill God's law in exactly the same way as a Christian does, by participating in the New Covenant promise of that law being written in the heart and mind. So the answer to your question is, No.
Now you might wonder how someone during OT times could be part of the New Covenant. But that's for another time.