Is it Othello's jealousy or Iago's jealousy that brings the downfall of Othello?

This question could be argued either way. It is initially Iago's jealousy that sets off the chain of events in the play, but Othello falls into Iago's trap and, by the end of the play, he has become so jealous that he kills Desdemona over her imagined infidelity.
At the very start of the play, Iago already demonstrates the jealousy that he harbors against Cassio and Othello. Iago resents the fact that Cassio has been made a lieutenant. He says that Cassio is

Mere prattle without practice / [...]But he, sir, had th’ election; / And I, of whom his eyes had seen the proof / At Rhodes, at Cyprus, and on other grounds /Christened and heathen, must be beleed and calmed /By debitor and creditor.(1.1.27-32)

Iago complains that he knows more about battle than Cassio does, and yet Othello has promoted Cassio over him.
Iago is jealous of Cassio, but he is also jealous of Othello. He says a few scenes later that "I hate the Moor, / And it is thought abroad that ’twixt my sheets / ’Has done my office" (1.3.429-431). For some reason, Iago believes that there is a rumor that Othello has been sleeping with Iago's wife. Although Iago has nothing to substantiate this, the envy that he has over Othello's position, the snub that he feels at Cassio being promoted, and the hint that his wife might be unfaithful is enough for Iago to decide to ruin Othello's life.
Iago decides to "put the Moor / At least into a jealousy so strong / That judgment cannot cure" (2.1.322-324). After Iago introduces his false suspicions about Desdemona, he and Othello have a conversation in which the word jealousy is brought up 7 times in a span of 60 lines (3.3.170-260). Ironically, Iago warns Othello not to be jealous, but this is exactly what he's trying to get Othello to do.
Othello swears that he will not allow himself to become prey to jealousy (3.3.207-223), but he has already fallen into Iago's trap. The jealously drives him into a rage, and he ends up killing Desdemona. In his last speech, he admits that he "loved not wisely, but too well" (5.2.404).
https://www.folgerdigitaltexts.org/html/Oth.html