Once I read your sentences I felt a difference between them which I could not explain exactly. If I were to rewrite those 2 sentences I would write:
1- possibly this is a good idea.
2- In my opinion this is a good idea.
I think that the stress in "I believe this to be good idea" is more on the idea itself. In the second sentence ("I believe this is a good idea") there is more stress on your opinion than the first sentence. I also recommend you to take a look at this page:
Definition and pronunciation of believe | Oxford Advanced Learners Dictionary