What is the difference between the "Passive form" and "게 되다"?
To me, these sentences have the same meaning.

행복하게 됬어요 (I became happy.)
행복해졌어요 (I became happy.)

Maybe there be a nuance of "there was no other way but..." when we are using 게 되다 but I'm not sure.

Thanks~
고맙습니닷 ♥

Question

What is the difference between the "Passive form" and "게 되다"?
To me, these sentences have the same meaning.

행복하게 됬어요 (I became happy.)
행복해졌어요 (I became happy.)

Maybe there be a nuance of "there was no other way but..." when we are using 게 되다 but I'm not sure.

Thanks~
고맙습니닷 ♥

Answer

There is a difference between them in meaning and usage.

1. -지다:   become or get/grow (usually indicates direct consequence).
  작아지다 (became smaller), 나빠지다 (got/grew worse)
  얼굴이 빨개지다 (complexion got reddish == blush)
  그는 부유해졌다 = He got rich.

2. -게 되다:  come to an action or state (through some arrangement or requirements); come to be
  서울에 있는 학교에 가게 되다 = I got to attend a school in Seoul.
  일본에 출장을 가게 되다 = It came to be that I have to take a business trip to Japan.

The above shows the most common cases, but sometimes they can be use with similar meaning.

Between 행복하게 되었어요 and 행복해졌어요, both can work but the latter sounds more natural to me.