-ㄴ다는 듯이 = -다[고 하-] + -는 듯이 -다[고 하-] is an abbreviated indirect quotation -는 듯이 means "like, as, giving the appearance of ...; appearing (to be), looking (like); seeming as if" So, -ㄴ다는 듯이 means "as if to say ... ; like, as, giving the appearance as if to say ..." -ㄴ다는 듯이 is used for more apparent situation than -는 듯이. 그 사람은 반가운 듯이 내 손을 잡았다. He hold my hands as if he was glad to see me.(50% possibility) 그 사람은 반갑다는 듯이 내 손을 잡았다. He hold my hands as if to say he was to see me.(90% possibility)

저는 한국인인데 차이 거의 없는 것 같아요. 다른 분이 단 댓글이 맞는 것 같아요.

I’m not Korean, but I’ll add what i think. 반가운 듯이 = as if they were friendly 반갑다는 듯이 = as if they were said to be friendly or 반갑다고 하는 듯이 (hard to translate 한다는 것 meaning) So, I think the difference is that the first one they ARE known to be friendly towards each other, and 반갑다는 듯이 is like “they are SAID to be friendly” or people THINK they are friendly.