AFAIK Nihon-shiki is designed to reflect the Japanese kanas and their traditional regular arrangement as close as possible - note that it also uses e.g. "tu" for ツ.
OTOH Polivanov seemingly tried to reflect actual pronunciation, thus ツ is "цу" (tsu), ふ is "фу" (fu), を is "о", は is "ва" (va) when it's a particle, the syllabic nasal is "m" in environments where it is so pronounced etc.
The only real mystery about Polivanov system from this perspective is why ち is "ти" (ti) and not "чи" (chi).
OTOH Polivanov seemingly tried to reflect actual pronunciation, thus ツ is "цу" (tsu), ふ is "фу" (fu), を is "о", は is "ва" (va) when it's a particle, the syllabic nasal is "m" in environments where it is so pronounced etc.
The only real mystery about Polivanov system from this perspective is why ち is "ти" (ti) and not "чи" (chi).