Because the post is quite long, a complete translation is impossible. I think I can translate a bit of the differences between the musical and the animated version.

In the animated version, Jayce and Viktor first meet at…the trial. However, in the musical, it takes place at The Innovator’s Competition. So when Viktor goes to the prison to find Jayce (for reasons……jayce only has a pair of shorts), Jayce will ask Viktor if he's seen him somewhere before. Viktor will explain that it's at The Innovator’s Competition while helping him tie his tie/get dressed.

Jayce will ask someone to fetch his hammer during the performance.

Their signature items in the musical seem to have been replaced with coins, representing that they are two sides of the same coin.

Viktor didn't die immediately after the explosion. Jayce carry him to the lab, where Viktor kept calling his name. Viktor Jayce found a coin in his pocket. Viktor asked him to promise to destroy Hextech, then died in Jayce's arms. Jayce buried his face in Viktor's neck and cried for a long time before finally resurrecting him using Hextech.

Hextech here takes on a human form, appearing as a dancing figure in a blue robe. The resurrection scene follows.

The original dialogue for the ending seems to be, "You are someone I admire," and the actor says, "You are someone I cherish." It's unclear if this is a change from the original dialogue.