Each of the books of the New Testament is well preserved as can be seen using the tools of historical research. Historical research, however, can only get us so far with respect to the Old Testament. For example, until recently the oldest Hebrew manuscripts of the Old Testament were not very old, and the oldest Greek manuscripts of the Old Testament were only about as old as the oldest Greek manuscripts of the New Testament. The Dead Sea Scrolls helped the situation out somewhat. Nevertheless, we have no large segments of the Old Testament Scriptures that can be dated to before the 6th century B.C. (before the captivity in Babylon). Moses, however, wrote the first books of Scripture hundreds of years before that, perhaps even a thousand years before that.
Moreover, while the Dead Sea Scrolls were an amazing archaeological find that boosted our knowledge of the state of the text in ancient times, it represents a geographically non-diverse transmission. Likewise, while the Masoretes (especially in the medieval period) were fastidious, they also left a very controlled transmission of the text.
The Septuagint transmission is slightly more interesting than that of the MT. The LXX, however, at best represents a post-inspiration translation of the text - and its early transmission is shrouded in legend.
All that said, it would be great if we could know that the text of Moses had survived substantially intact down to the days of Jesus.
And we can know that. Abraham said, "They have Moses." That wouldn't be true if they did not have the Torah. Recall that Jesus recounts in the parable of Lazarus:
Abraham saith unto him, "They have Moses and the prophets; let them hear them."
Moreover, Jesus and the apostles appealed constantly to the Old Testament Scriptures. Likewise, Jesus told the Pharisees:
Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me.
They could not testify to Jesus if they did not exist.
Thus, while we may be unable to provide historical proof that the Old Testament Scriptures are in the form they existed before the 6th century B.C., we can demonstrate from Jesus' own testimony that they were intact in his day. Moreover, we know what they said in Jesus' day. Therefore, we can have confidence that we have a well-preserved Old Testament and not only a well-preserved New Testament.