And yet God sees the 'new and better' as a fulfillment of the law of Moses, not as something that competes with or demolishes the law of Moses.
Look at this....
1 Corinthians 5:7-8
Christ, our
Passover lamb, has been sacrificed.
8Therefore let us keep
the Festival, not with the old bread leavened with malice and wickedness, but with the unleavened bread of sincerity and truth.
What
Passover, and what
Festival of Unleavened Bread is he talking about? The Mosaic ones, of course. We 'keep' those laws (not a 'new' law) in the new way of Faith in Christ, and walking in the Spirit. Faith in Christ applies the Sacrifice of Jesus to us so that God looks at us and says, "I see no debt of law concerning the requirement for a Mosaic Passover". And when we walk in the Spirit in obedience to God, summarized in the Mosaic command to 'love your neighbor as yourself', God looks at us and says, "I find no debt of law concerning the Mosaic requirement to rid one's house of leaven" (remember, leaven is a type and shadow of sin).
The Mosaic laws of Passover and the Feast of Unleavened Bread which immediately follows it find their fulfillment in Christ, not their destruction as the church teaches. God even saying we've met the obligations of the Mosaic law. A changed law, yes. A totally new and different law? No.