I understood it 'as' threat. と I understood it 'to be' threat. はどう違いますか？説明が難しい場合は、例文を教えて下さい。

As far as I'm concerned they mean exactly the same thing. "I understood it to be a threat" allows the speaker to place more emphasis on "be" (since it employs two syllables and it sounds kinda dumb to place emphasis on "as" in the previous sentence).
So you could place emphasis such as
Questioner: "What made you draw your weapon?"
Answerer: "We were arguing heatedly. I saw the man place his hands in his pockets and I took it as a threat"
Questioner: "As it turns out though, he was reaching for his keys. He didn't have a gun or weapon of any kind for that matter"
Answerer: "That may be the case, but he was told me he was going to kill me. He was yelling like crazy. From the way he was spitting mad, when he reached into his pockets I figured he had a gun and so naturally I took it to BE a threat"