듯 and 듯하다 come after the adjetival form of the past (-(으)ㄴ), present (는), furure (-(으)ㄹ), and the modal ending (겠는). So to know the difference between -ㄹ and -겠는, you need to know the use of the sentence endings -겠다 and -(으)ㄹ 것이다 from which those forms deriveq from.
-ㄹ 것이다 represents the normal future, like 'will' in English. -겠다 is like the modal verbs would, might, or could, and adds the speaker's intention (will, would - 1st person) or uncertain likelihood (could, might - 3rd person). So for the third person case,, the difference is normal future vs more uncertain possibility (e.g. 이 개는 죽을 거야 = normal (This dog is going to die), 이 개는 죽겠어 = modal (This dog might die).
This difference carries over to to 듯하 다 as well.
1. 개가 덤벼들 듯이 으르렁거린다 = (future) The dog growls as if it was about to attack.
2. 영철이는 모르는 듯ㅏ다 = (present) 영철 looks like he doesn't know.
3. 영철이는 답을 모르겠는 듯이 우물쭈물한다 = (modal) 영철 hesitates as if he can't seem to come up with ananswer.
#1 and #2 express the simple sense in the future and present tense, whereas #3 is more nuanced. 겠는 adds the sense that he is trying to remember or fugure it out but cannot give the answer. So 1 and #2 are suitable for questions about simple facts while #3 can apply to more complex questions that require thinking. 겠는 adds this sense of (not) being able or likely to do something, as contrasted with simple determination. It is thus a more detailed expression than the others. However, note that 듯하다 with 겠는 is pretry uncommon compared with the other plain forms.