Sometimes I hear it said that Old Testament ethics can be summed up in the command to fear God, and New Testament ethics can be summed up in the command to love God.
Related, it is sometimes observed that the Old Testament summary of the law is ten sentences that prohibit ("Thou shalt not" - those making this point usually do so quoting the old fashioned way of putting that), whereas the New Testament command is two sentences that are about love ("Love the Lord your God with all …; love your neighbour as yourself".)
I've commented before about one aspect of this. The ten commandments may sound negative because they are framed in negative form. However they are actually extremely liberating for that very reason.
What comes from which Testament?
Let's look more closely at this. Firstly, let's get our bearings right, and make sure we're clear what is said in which Testament.
Take Jesus' "two greatest commands", to love God and neighbour. Take a look at one of the passages where we find these, such as Matthew 22:34-40. The context is Jesus being tested by the Pharisees, who are looking to trip him up with a trick question. They ask "Which is the greatest commandment in the law?". Here's how the trap works: If Jesus singles out a single Old Testament command as "greatest" they can accuse him of playing down other parts of the Old Testament. If he refuses to answer the question, he looks ignorant.
So what does he do? He gives two Old Testament commands that function as summaries within the Old Testament itself. He quotes Deuteronomy 6:5 ("Love the Lord your God") and Leviticus 19:18 ("Love your neighbour as yourself"). He's avoided the trap, because the commands he give function as summary commands in their Old Testament context. (Deuteronomy 6:1-6 is a headline for that whole section of Deuteronomy, and Leviticus 19:18 is a summary of the whole of Leviticus 19 and all the other "neighbour" commands in Leviticus.
At which point, we notice that Jesus' two greatest commandments are themselves Old Testament commands. It's not that the Old Testament summarises itself with the ten commandments, whereas the New Testament summarises its requirements with two laws to love. There is more than one summary of God's requirements within the Old Testament. One summary is the ten commandments, and the other are the two commands that Jesus selects. So this isn't a contrast between Old and New at all.
We should also notice, in passing, that Jesus explicitly reinforces about half of the ten commandments in Matthew 5. Those commandments are not only summaries within the Old Testament; Jesus himself regards them as another way to summarise the Old Testament law.
We could also turn to a passage like 1 Peter 1:17 to notice that the command to fear God is not only an Old Testament command, but it occurs in the New as well.
Looking more closely at Deuteronomy 6
So, the command to love God with all our heart, soul, [mind] and strength comes from Deuteronomy 6. Let's look at that chapter a little more closely to see what this "love for God", the heart of New Testament ethics, means.
We have to start with Deuteronomy 6:1. "These are the commands, decrees and laws the Lord your God directed me to teach you to observe in the land that you are crossing the Jordan to possess." My view is that "these" is primarily forward-looking here, looking on into chapters 6 and following, rather than back into chapter 5. Chapters 1-4 narrated Israel's journey by which they reached the plains of Moab. Chapter 5 gave the people the Decalogue, the ten words which God spoke with his own voice and wrote with his own finger. The people begged not to hear any more, they were too frightened, so Moses was given the rest to pass on. And chapters 6 and following are what he was told.
Why is he to pass these commands on to the Israelites? Deuteronomy 6:2: "… so that you, your children and their children after them may fear the Lord your God as long as you live, by keeping all his decrees and commands that I give you." The goal is that the people of God fear the Lord their God, and that they do so down the generations. Fear is primarily about respect, rather than about "being frightened". The people will show proper respect for their God by keeping his commands. As Moses passes these onto them now, so they must pass them on to their children, and so on for all generations.
Verse 3 ties this in to long life in the land, and then we get verses 5 and 6: "Hear, O Israel, the Lord our God, the Lord is one. Love the Lord your God with all your heart and with all your soul and with all your strength." Here's the headline command that sums up all the commands by which they must live, if they are rightly to fear / reverence the Lord their God: Love him with all your heart, soul and strength.
Verses 7 to 8 then continue the theme of passing these commands down the generations, and verse 9 and following expound the dangers of forgetting God once they're in the land.
Two things follow from this.
Don't set love in opposition to fear
Here's the key point from the argument in Deuteronomy 6: The commands God gives are the way they are to fear him. The command to love is the summary of all the other detailed commands they will be given. So the command to love is, in summary form, the way they are to live in fear of God.
"Fear the Lord your God" and "Love the Lord your God" are not two opposing approaches to life and to God — love versus fear. Fear means right respect, dignity and reverence toward God. It is only indirectly about being frightened. You can see someone who fears God because they will be a person who loves God.
So we must not set love and fear against each other, making one desirable and one not, or one Old Testament and one New Testament. We fear God by loving him. We love God in order to fear him rightly.
Don't set love in opposition to obedience
But how do we love God? If it's tempting to set fear and love against each other, it's equally tempting to set fear and obedience against each other. The Old Testament was about commands, we say, whereas the New Testament is about love for God.
We've just seen in Deuteronomy 6 that the command to "love the Lord your God" is a summary of all the detailed laws that will follow. We need to complete the chain. We fear God by loving him. And we love God by doing what he commands.