This question is a very important one. Quite often people ask a different question, which is: "In which way is the new covenant different to the old covenant?". Many times people holding to classical Baptist theology, they attempt to maintain that there is a gulf of difference between the old and the new covenants. This is done to uphold their view of believer's baptism which has no shadow in the old testament for them in their understanding. We hold to a covenantal view of baptism for the baptism of adults who profess faith for the first time and the children of believers. It is important to know that the old testament covenants are the same in substance to the new covenant, but different in their administration.
Which book of the Bible especially handles the old versus new covenant question? It is the book of Hebrews. Note I called it the Book of Hebrews and not the epistle to the Hebrews. It is deliberate because it does not bear the hallmark of an epistle. As a side note I am firmly that convinced that Paul was the author, which is how the church father's understood the authorship of this book also.
Hebrews mentions the word better of Superior many times and this book teaches us that the New covenant ratified through Jesus Christ is superior in every way.
A key word is Superior or better which is κρείττων. It is found in Hebrews:
1:4 Christ is superior to angels
7:7 Melchizedek is superior to Abram
7:19 a better hope
7:22 a better covenant
8:6 better promises
9:23 we are purified with better sacrifices that the old covenant
10:34 a better possesion and an abiding one
11:16 a better country
11:35 a better life
11:40 God had prepared something better for us.
12:24 the blood of Jesus speaks a better word than the blood of Abel
Let us rejoice that we have the covenants fulfilled from the old testament fulfilled through Jesus Christ God's Son in the new covenant. If you would like further reading, may I recommend O. Palmer Robertson's Christ of the Covenants.