They means the same, however, the subjects for these two sentences are different for the transitive and intransitive verb. I think there is "if (もし) clause" before these sentences and to compare them, I would write: (with literal translations) (私は)私の答えを変えていたでしょう。(I would change / would have changed my answer.) 私の答えが変わっていたでしょう。(My answer would change / would have changed.) or (私は)私の答えを変えたでしょう。(I would change / would have changed my answer.) 私の答えが変わったでしょう。(My answer would change / would have changed.) *I think the translations of た and いた (of 変わった and 変わっていた) are the same in English though I'm not very sure for my English. I hope other people answer to you. I hope this helps you.