The contradiction of these passages is not in how Judas died (that can be debated), but in the other details of the story. The verses in question are Matthew 27 3-10:

(3) When Judas, who had betrayed him, saw that Jesus was condemned, he was seized with remorse and returned the thirty silver coins to the chief priests and the elders.
(4) “I have sinned,” he said, “for I have betrayed innocent blood.” “What is that to us?” they replied. “That’s your responsibility.”
(5) So Judas threw the money into the temple and left. Then he went away and hanged himself.
(6) The chief priests picked up the coins and said, “It is against the law to put this into the treasury, since it is blood money.”
(7) So they decided to use the money to buy the potter’s field as a burial place for foreigners.
(8)That is why it has been called the Field of Blood to this day.
(9)Then what was spoken by Jeremiah the prophet was fulfilled: “They took the thirty silver coins, the price set on him by the people of Israel,
(10) and they used them to buy the potter’s field, as the Lord commanded me.” [NIV]

and Acts 1 18-19:

(18)(With the reward he got for his wickedness, Judas bought a field; there he fell headlong, his body burst open and all his intestines spilled out.
(19)Everyone in Jerusalem heard about this, so they called that field in their language Akeldama, that is, Field of Blood.) [NIV]

Who bought the field, what did Judas do with the money, and how did the field come to get the name “Field of Blood”?

Did you not read the information provided by Apok to Kevin from Tekton Apologetics Ministries? It is very interesting, to say the least. And I think that it offers some explanations to this alleged contradiction that are more than adequate. And I agree with Kevin; the third explanation is the most likely, and it is uber-typical of Jewish literary style.
“…Matthew’s creative use of an OT “type”.
This would combine the idea that Matthew is not actually describing Judas’ death, with Matthew’s use of the OT texts as typologies. Audrey Conrad, in “The Fate of Judas” (Toronto Journal of Theology [7] 1992), notes that Matthew’s unique words “departed” and “hanged himself” are found in combination in another place in the LXX:
2 Samuel 17:23 And when Ahithophel saw that his counsel was not followed, he saddled his ass, and arose, and gat him home to his house, to his city, and put his household in order, and hanged himself, and died, and was buried in the sepulchre of his father.
Conrad notes that rabbinic interpretation of Ps. 41:9 (”Yea, mine own familiar friend, in whom I trusted, which did eat of my bread, hath lifted up his heel against me.”) thought that Ahithophel was the traitor David was describing — and of course this same verse was applied by Jesus to Judas (John 13:18). Conrad still thinks there are not enough parallels (!) but we would maintain that the parallels are sufficient, and that Matthew is indeed alluding to the traitor Ahithophel in this passage, and is therefore NOT telling us that Judas indeed hung himself, but that Judas fulfilled the “type” of Ahithophel by being a traitor who responded with grief and then died. Matthew is thereby making no statement at all about Judas’ mode of death, and Luke’s “swelling up” stands alone as a specific description of what happened.”

In other words, Matthew was describing the death of Ahithophel as documented in the OT. This would make even more sense when we consider the fact that Matthew’s gospel was written to the Jews for purposes of testifying to them, specifically, of the messianic quality of Jesus Christ.

As much as the Jews studied the OT (heck, they could quote the entire Torah by the time they were 5), they did not understand it. This was the “vail” that Paul refers to in some NT epistles, having been pulled over the eyes of the Jews for the sake of the gentiles. Matthew could have easily been alluding to Ahithophel because of the interpretation to which Jewish scholars of that day gave to Psalm 41:9, which aluded to Christ’s betrayal, but which the Jews, up until the arrival of Christ, and indeed even afterward (and indeed even today), interpretted as referring to the betrayal of David by Ahithophel.
It is important to note that David went through many things in his life that were a “TYPE”, i.e. a shadow of Christs life and sufferings. There are many references in the NT to the book of Psalms in the context of prophecy and type.
It is also important to note that in the original Greek language, there are no quotation marks (in fact, for the longest time everything was in capital letters with no spaces, as well!). That means that if a writer is quoting something, for instance the old testament, there are only a few clues that will indicate this:
1) If you are familiar with what the writer is quoting, you may recognize that he is quoting the passage.
2) He might (read: might) begin the quoted passage with the term which we translate as “that”. For example, in english, one might say “The boy said ‘I want to go to the store.’”, or one might say “The boy said that he wants to go to the store.” This use of the term “that” is largely the best clue that you will ever get in Greek, and it is not rare to be deprived of even that.
So, this could easily be a failure on the part of the translator. On the other hand, Matthew may have been using this type as a metaphor, not intending it to be a direct quote. In either case, this type would have served to call something important concerning prophecy to the attention of the Jews.
This is the position that I take, and I think there is little doubt that this is what Matthew is doing for anyone who has taken enough time in the study of the scriptures to understand how the life and death of Christ is foreshadowed and described throughout all of the Old and New Testament, especially by Helenist Jews.
As far as who bought the field…that is far easier to explain, and once again, I think that the information provided in Apok’s link does an adequate job of explaining it. This time, however, I won’t quote the information, because it is easy enough to explain without doing so.
Judas never bought the field himself. However, he did give the money back to the priests that had been given to him to betray Christ. It was against their law for the priests to except this money and put it back into the temple treasury, because it was blood money (ironic, I know). So they bought the field where Judas hung himself.
So why does one passage say that the priests bought the field, while another said that Judas bought the field? Isn’t it obvious by now? The priests were never allowed to claim the money as theirs after it entered the possession of Judas. They may have bought the field, but they did it on Judas’ behalf. Not that Judas was some great friend of theirs that they wanted to take care of, but they had to do something with the money, and whatever was done with it had to be done on behalf of Judas; otherwise the money would’ve technically belonged to them.
If you gave me money to go buy something for you, I can say that I bought it, or I can say that you bought it. In either case, what was bought belongs to you.
So, we see clearly, that both are true. It is true that Judas bought the field, while it is also true that the priests bought the field. In both cases, the field belongs to Judas.

The priests used the field as a graveyard for foreigners according to Matthew. This would mean that they were acting as if it was theirs (but not necessarily belonging to the Temple). So, the plot of land would be in the care of the priests and not in Judas’. Since everyone in Jerusalem knew about the field according to Luke (Acts), they would have known that the priests tended it and that it was in reality, theirs although they may have put the plot in Judas’ name.

This is unrelated to who bought the field or who owned it. The priests could have performed a pagan ritual and gave homage to baal on this field after Judas died for all we care. This alleged demonic sacrifice might have stirred the Jewish people to drag the priests behind horsedrawn carriages by their winkies for all of Rome to witness, and Pilate might have sat on his porch spewing wine from his nostrils laughing at the spectacle. What happened after the field was purchased or after Judas killed himself is beyond the scope of this discussion.
If you disagree with me, then I would interject this suggestion: nothing would have stopped the Jew from buying this field from Judas after his death with the temple money; there would be nothing unlawful about that. This is why I say it is irrelevant; there is any number of things that could have happened to reconsile this “doubt”; it does nothing to detract from the former proposition.
As for the alleged contradiction in the reason for the field’s name. One passage says it was called “field of blood” because Judas died there, while another says that is was called as such either because it was purchased with blood money, or because it was made into a graveyard (the interpretation of this passage is debateable). Both reasons can easily be true. Haven’t you ever had more than one reason for doing something? Are you then contradicting yourself, or do you just have more than one reason, and that’s that?
The term “Aceldama” has aramaic origins. It was commonly used to mean “a battle field” or “a field where much blood was shed”. It could also be used, and indeed was used, to mean “graveyard”, especially for foreigners who died in Jerusalem, no doubt they often died unusually or violently.
Matthew 27:5-8 documents the event. However, it is debated as to whether this passage is saying that the label was given because of the blood money, or because it was a burial place for foreigners.
In either case, the initial reason that this field was labeled as such was probably because that is where Judas’ body was found. Everyone in Jerusalem heard about Judas’ suicide (Acts 1:18-19), so they called the field where he died “Akeldema”. Later on, however, after the priest purchased the field, the people learned one or both of two facts:
1) that the priests purchased the field and made it into a graveyard for foreigners…
and/or
2) that the priests use the blood money to purchase it with (imo, it is unlikely that this is why it was named as such. I think it is reason #1 alone …examine the text and do some research on the usage of the terms “Akeldema” and “field of blood” )
In either case, many other people adopted the same name for the field, for one or both of these new and different reasons.
You may say “unlikely story”, but this would not be the first or the last time that something like this has happened. Some people start calling the field something for one reason, while other people, who have different (but also true) knowledge concerning the field, hear the reference, and, perhaps not understanding the original reason for the name, adopt the reference for their own reasons.
This is for sure: two things occured…the spilling of Judas’ blood upon the field, and the priests buying the field with the blood money and using the field as a graveyard for foreigners. It is unarguable that both of these are good reasons for calling this field “Akeldema”. How unlikely is it that there were two different groups of people who adopted this name for the field for two different reasons, especially if one group heard the other group using the term, and didn’t know their reasons? Even if they did know their reasons, they could still just as easily adopt the term for their own reasons.

And lastly, this also is for sure: it is unarguable that it is not impossible, indeed not even improbable, that both of these passages can be true without contradiction.