The Four Horsemen are the ones who will bring the apocalypse. Are they under the command of the devil? Are they more powerful than the devil?
This depends on your definition of "power."
2: I looked, and there was a white horse, and its rider had a bow. He was given a crown, and he rode forth victorious to further his victories.
4: Another horse came out, a red one. Its rider was given power to take peace away from the earth, so that people would slaughter one another. And he was given a huge sword.
5: When he broke open the third seal, I heard the third living creature cry out, "Come forward." I looked, and there was a black horse, and its rider held a scale in his hand.
8: I looked, and there was a pale green horse. Its rider was named Death, and Hades accompanied him. They were given authority over a quarter of the earth, to kill with sword, famine and plague, and by means of the beasts of the earth.
Note that the passage does not state who or what gave them this power: was it the Devil acting via proxy? Was it the Wrath of God? There are myths about this, but the question is specifically asking about the Christian apocalypse which implies source material would have to be in the book of Revelation.
What we can infer from this:
The Horsemen were destructive in nature: this goes against the nature of God as defined in the new testament as being a kinder, gentler diety compared to the old testament. Clearly their power must derive from evil, but we do not know their origin. This makes it difficult to measure them against the Devil: i.e. if Satan created them we might know they are strictly lesser in power.
The Horsemen are able to affect earth directly by killing, starving, and infecting men. In verse 4, we learn that War is able to cause men to fight each other.
What do we know about the Devil?
He is one of God's archangels, fallen from heaven. He clearly must be powerful, and evil.
Numerous times throughout the Bible, we see the Devil act. However, he never actually does anything. His power is that of suggestion and temptation. In Genesis he tempts Eve to eat the forbidden fruit, so she will cause the fall of man from grace. In the Gospels he tempts Jesus multiple times, but is unable to sway him or to harm him.
Genesis 3 shows the snake is "cunning" and tricks Eve:
1: Now the snake was the most cunning of all the wild animals that the LORD God had made. He asked the woman, "Did God really say, 'You shall not eat from any of the trees in the garden'?"
. . .
13: The LORD God then asked the woman: What is this you have done? The woman answered, "The snake tricked me, so I ate it."
This great deceiver, the serpent, is later identified to be the Devil in Revelation 12:9:
The huge dragon, the ancient serpent, who is called the Devil and Satan, who deceived the whole world, was thrown down to earth, and its angels were thrown down with it.
The Devil persuades Eve to commit the original sin without actually doing anything other than talking.
In Matthew 4, we see the Devil tempt Jesus:
1: Then Jesus was led by the Spirit into the desert to be tempted by the devil.
3: The tempter approached and said to him, "If you are the Son of God, command that these stones become loaves of bread."
5-6: Then the devil took him to the holy city, and made him stand on the parapet of the temple, 6and said to him, "If you are the Son of God, throw yourself down..."
8-9: Then the devil took him up to a very high mountain, and showed him all the kingdoms of the world in their magnificence, and he said to him, "All these I shall give to you, if you will prostrate yourself and worship me."
10: At this, Jesus said to him, "Get away, Satan! ..."
Jesus specifically identifies the tempter as Satan, the Devil. All he can do is suggest to Jesus that he do certain things: he did not make Jesus turn rocks into bread, or jump off a roof safely. His power is clearly that of suggestion and temptation.
Given what we know, how do they compare?
If we measure known quantities about where they came from, the Devil is likely more powerful. He is a fallen archangel, one of God's lieutenants. We know almost nothing (in scripture) about the origin of the Horsemen: this implies they are not major players in the grand scheme of things.
If we measure what they are capable of actually doing, the Horsemen are likely more powerful. They can directly impact earth, killing people either directly via sword, famine or disease, or by causing mayhem wherein men kill each other. The Devil can merely suggest that men cause themselves to fall from grace.
With very few exceptions throughout history, Christian theology has unanimously believed there is but one omnipotent being: 'God' (Yahweh, the god of Israel), who created all things, including the angelic being who would come to be known as 'the satan'. No matter how we might define 'power', it is consistent throughout the whole stream of Christian beliefs, legends, folklores, and myths that the devil's power is limited while God's power is unlimited.
To get to the original question, though, we want to clarify how 'powerful' the satan is relative to the four horsemen found in the Book of Revelation. Muddying this question, however, is which version of the satan are we looking at? Even within the whole canon of Christian scriptures, the satan is not depicted consistently. In the Hebrew bible the satan makes but three appearances, in the books of Job, Chronicles, and Zechariah. In none of these text is the satan explicitly 'evil'; he is a sort of prosecutor acting on behalf of heaven's court, his mission to test and object to the faithfulness of God's people.
In later Second Temple-era literature, the satan begins to take on a more ominous role, becoming conflated with one of several angels who abandoned their home in heaven when the earth was young (an interpretation of Genesis 6.1-4 popular by the first century BC). By the time of the earliest Christian era, apocalyptic Jews perceived the satan as a fallen angel or a demon. In apocalyptic thought, the satan is the archetype of evil, his influence wide, but nevertheless doomed to fail in the eschaton. This is the satan we see in the Revelation, and the version we should stick with.
Conveyed through the Revelation's symbolism, the satan antagonizes Israel (the woman in Rev 12), inspires the brutal idolatry of Rome's emperor cult (the two beasts in Rev 13-19), and must be restrained to prevent similar influences from spreading across the earth (the dragon's imprisonment in Rev 20). For the author of the Revelation, the satan is dangerous because he causes violent hatred and greed in the world's empires.
The four horsemen
The four horsemen are not four literal people riding horses.
As I pointed out in an answer to another question, the Revelation's symbolism runs deep, and the four horsemen are an amalgam of symbols and concepts drawn from across the Hebrew bible:
Ezekiel 1-7 has the prophet see a vision of God on his throne, holding in his right hand a scroll with writing on its front and back. The scroll, Ezekiel is told, represents God's judgment against the kingdom of Judah for the people violating their covenant with him. Ezekiel receives the scroll, ingests it, and then speaks its message of judgment against his fellow Judeans. A handful of times he warns about 'the sword', 'pestilence', 'famine', and even 'wild animals'. This cluster of disasters — war, plague, famine, and attacks from wild animals — comes from a common tradition seen throughout Hebrew prophetic literature. It is encapsulated in Leviticus 26, a chapter that warns these exact things will fall on the Hebrews if they do evil and disobey God.
A century and a half later, Zechariah 1 has another prophet receive a vision of four men/angels riding four differently colored horses. In chapter 6, the prophet sees four chariots drawn by four differently colored horses. The two visions each symbolize judgment against the Judeans' enemy, Babylon.
Revelation 4-6 combines parts of the vision of Ezekiel 1-7 with parts of the visions of Zechariah 1 and 6, to make a new scene: The revelator sees a vision of God on his throne, holding in his hand a scroll with writing on its front and back. The revelator sees a slain lamb (Jesus) receive the scroll and begin to break the wax seals keeping it shut. As each seal is broken, more of the scroll's contents are revealed. The first four revelations are symbolized as four men/angels riding four differently colored horses. They carry authority to enact a cluster of disasters — war, plague, famine, and attacks from wild animals — and are given instructions from either God or Jesus (Rev 6.6, 'a voice in the middle of the four living creatures', being the location of God's throne).
Based on the sources the revelator depends on to form his vision in Revelation 6, the four horsemen appear to symbolize various judgments from God. The likely target of these judgments is the forces of evil identified in Revelation 12-19: the dragon (the satan), the two beasts (the Roman Empire and its emperor cult), Babylon (Rome itself), and 'the kings of the earth' (a general catch-all for world leaders and nations that ally with Rome's ideology).
The Revelation is a Second Temple-period apocalypse. Although these apocalypses carried explicitly dualistic themes of good and evil, the authors were not ditheistic: no evildoer can ultimately match God; it is guaranteed that good will triumph over evil.
For the four horsemen to represent God's judgment against evil forces, including the satan, this would make the four horsemen 'more powerful than the devil' as far as the revelator is concerned.