From the point of view of grammar, it seems to me that you can also omit the "who is" in the second example. The essential difference I see is that logically there's always a responsible person, but there may not always be an angry person. In the second example, you're making a judgement which may or may not be true.
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AnonymousIn participle constructions, the relative pronoun and the auxiliary can sometimes be omitted, often also before adjectives.Why are you asking about participle constructions when neither of your examples contain participles?
1. He's the man (who is) responsible for all the paperwork.
2. She's the woman who is angry at me.