During the Roman Empire there were slaves taken from all over but then during the Middle Ages, there was feudalism - which can be seen as slavery without the buying and selling of people as property. From feudalism it transformed into bastard feudalism where they charged people rent to work the land.
Why would the landowners decide that feudalism was a better economic option than slavery?
The process you are describing - replacing slaves with tenant farmers for agriculture work happened before the events we call "the collapse of the Western Roman Empire". By the time of Constantine the Great it was pretty much already prevalent so it was codified in the laws.
Source: "The Cambridge Medieval History" - J.B. Bury, etc.
So I'm just going to assume that your definition of feudalism is more along the lines of the Marxist conception, specifically that of tenancy and rent, as opposed to the mishmash of assumptions revolving around the supposed reciprocal obligations of land for loyalty between the military aristocracy.
One of the key issues with your question actually depends entirely upon the definition of slavery, and arguments as to why or whether landowners stopped owning slaves, is entirely dependent upon what you count as "slavery."
For example, is a slave merely an unfree person who is deprived of the right to move and is bound to and under the legal subjection of a lord? If so, then one could argue that landowners never stopped owning slaves, and that serfs were slaves well into the middle ages.
On the other hand, you could define a slave as specific to a mode of production, someone working on a slave plantation, where his production is directed by overseers, and his lord otherwise provides the necessity of life. If this is your definition, then slavery fell out of favor by the Roman Crisis of the 3rd century.
This distinction is key because in the first definition, what if you have two people, one who is legally a slave, and one who is not, whose actual activity end up being the same? They both work on lands, they both can't leave, they're both under the legal subjection of the lord, they both give their surplus to the lord, the only difference is that the free tenant can represent himself legally. But outside of this very specific legal framework, his life is hardly any different from the unfree tenant.
Whereas in the second case, the distinction between free and unfree is very clear. A free farmer decides what he wants to plant, though he has to give fixed surplus to the lord. An unfree plantation slave does not decide what he wants to plant, keeps nothing of what he produces, but the master has to feed and clothe the slave, incurring a cost for the master.
So it is from this difference, especially in the second case, that I most commonly see the disappearance of slavery being argued for.
Plantation slavery is expensive. It requires overseers because slaves escape, and steady economic growth to make those expensive slaves worthwhile. Because whether the economy is good or bad, those slaves have to be fed lest the slave owners lose their investment in the slaves.
Compare this to tenancy, where the lord merely takes a surplus. Which means no matter whether the economy is good or bad, the lord will always take something. Because the serf is working his own land, he's far less likely to escape. So long as the serf gives this surplus (whether in produce or corvee labor), most of the time he's left alone.
This is why it's been argued that tenancy/feudalism is the most prevalent economic system in history. It's also not an accident that after the demise of southern plantation slavery, that it shifted to exactly just such a tenancy arrangement for sharecroppers. And simultaneously why plantation slavery only lasted in the Roman Empire until the Crisis of the 3rd century. Once Pax Romana was over, there was no longer the steady economy to guarantee the high costs of plantation slavery.
However, this is only if you accept the difference between slave and free on the basis of "mode of production." If you prefer the legal definition, then this wouldn't answer your question, because as I said previously, one could argue landowners never stopped owning slaves.
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