-는 듯하다 and -는 듯싶다 practically have the same meaning.
듯하다 is more plain sounding (factual) while 듯싶다 is softer and more personal, but the difference is very small.
The others also have a similar meaning with a slight nuance difference.
I tend to translate them as follows, but it's more a personal preference than any established theory.
- -는 것 같다 = It seems that ... (것 = thing, fact, idea; 같다 = is similar to)
- -는가 보다 = [subject] appears to ... (보다 = to see, look as an independent verb, or "it appears" as an auxiliary)
- -는 모양이다 = It looks like ... (모양 = appearance, 모양이다 = it looks)
Examples:
- 날이 추워지는 듯하다 = ... 듯싶다 = 날이 추워지는가 보다 (evokes a sense of spontaneous perception).
- 강아지가 아픈 것 같다 (more judgment/conjecture than with -는 듯하다, -는 듯싶다, -는가 보다)
- 강아지가 아픈 모양이다 (모양이다 may be in between the two camps, somewhat closer to 것 같다)