~ㄴ다는 and ~는
* ~ㄴ다는 (것): captures the noun phrase as a quoted remark or a general idea or a concept.
* ~는 (것): treats the noun phrase more as a specific action or situation, with a tighter construction.
So when a formal or abstract notion is involved, ~ㄴ다는 is more appropriate, while for simple, specific actions, ~는 suffices. ~ㄴ다는 (and ~라는 for the special 이다) makes it more indirect and general, like the conjunctive "that ..." in English.
Examples:
- 날 더 이상 좋아하지 않는다는 그의 말 => It's quoted phrase, so must use ~ㄴ다는.
(... 않는 그의 말 would render it like "his remark which doesn't like me anymore", which is nonsense)
- 사람은 대부분 이성보다는 감정에 더 좌우된다는 사실 => a general statement (좌우되는 사실 would make it unclear).
- 이기는 것만이 능사는 아니다 => Winning is not everything. (이긴다는 것 would sound strange)
- 이긴다는 것은 무엇을 의미하는가 => What does it really mean to win? (이긴다는 것 is better)
- 이거 이렇게 하는 거 맞아? => Is this the right way to do it? (specific action - can't use 한다는 거).
배운다는 것은 언제나 즐거운 일이에요 / 배우는 것은 ... (both work equally well)
외국에 산다는 것은 가끔 힘들 때도 있어요 / 외국에 사는 ... (both work, but the latter seems better because 힘들 때도 makes it narrowly focused)