Three Russian conductors (it would be unkind to say 'well... two-and-a-half') in three Prokofiev cycles, and the best by some distance is by the 'half', Rostropovich. He can't keep a tempo (sometimes he does, in the 2nd Symphony for example). He can't maintain a perfect ensemble (sometimes he does, in the Gavotte of the 1st Symphony). He's sometimes in, fu, ri, atingly slooow (introduction to the 1930 4th Symphony). His orchestra is not the world's greatest. BUT. But there is, always, a PORTENT in what he does. He loves and understands this music, the players love him, and he and they, helped by a warm, translucent recording (though the reverb and balance can change between Symphonies and there are a couple of horrendously obvious edits) give us the greatness of this music as neither of the two 'professional' conductors do. Rozhdestvensky is brash and slapdash (he was a notoriously bored rehearser) and Kitajenko, after Rostropovich, slick and gutless - though good, to be fair, in the more lyrical music. Rozhdestvensky does not include the original 1930 4th Symphony, only the 1947 revision. The other two include both.
I've not heard Ozawa, Weller or Gergiev. Jarvi is not to my taste, though many prefer him. Individual Symphonies exist in wonderful recordings: Mravinsky in the 6th, Alsop in the 4th, Leinsdorf or Alsop in the 5th. But no-one, no-one wanted, NEEDED us to hear these pieces as Rostropovich did.