-더라고요 simply relates what one experienced, while 던데요 has the nuance of presenting it as something new or surprising, or even contradicting what the other person thinks.
- 뉴스에서 속상한 이야기를 들으면 기분이 안좋아지더라고요.(Natural - calmly relates one's experience)
- 뉴스에서 속상한 이야기를 들으면 기분이 안좋아지던데요. (Not natural because the subject is not newsworthy).
-던데요 예)
XX 씨 출장갔다고 했잖아요. 근데 오늘 아침에 자리에 있던데요 = I thought you said XX went on a business trip. But I saw him at his desk this morning. (Here -던데요 fits the context much better).