I think they both are fine. They are the exact same sentence in a slightly different order, so it's only a question of who does the regarding. If I were to really analyze it, I would interpret #1 more conveniently, to mean the public thought that was the most effective way to spend money.
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cho7712 In the active sentence, as-phrase functions more like a necessary element rather than an adjunct which goes for as-phrase in my origianl example.
cho7712My guess : this sentence seems to be odd because as-phrase should precede