Omitting "to be" from a sentence before adjective
In general, there is no difference, and the 'to be' is entirely optional.
However, I think in some cases there is a slight difference, in that the 'to be' makes it more clear that you're talking about a short term state rather than an inherent trait of the subject.
For example:
- "He seems cold" could mean he seems to be chilled or that he seems emotionally distant.
- "He seems to be cold" unambiguously means chilled.