I've read both Death Note and Monster manga and have seen all of Monster and a few eps of Death Note. Monster anime is almost exactly the same as the manga and Death Note seems like it will be too. So based on that... I would say Monster got stronger as the story progresses but Death Note got weaker. I found the Monster ending to be more satisfying overall. Both are great series. I wouldn't classify either as mystery but as psychological thrillers/drama.
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