There is certainly a range of opinions among the reviewers here as to the merits of these composer-played performances. So here are a few dissenting remarks of my own. I have to take issue with Amazon editorialist Leslie Gerber's characterization of Piero Coppola as a "hack" conductor. In addition to his work here in Prokofiev's 3rd Piano Concerto, Coppola left many very distinguished 78 rpm recordings: one of the earliest and best accounts of Bizet's "Carmen," a great reading of the Saint-Saens Organ Symphony, and many pathbreaking accounts of Debussy, Ravel, Roussel, etc.
As the typically well-written and informative review here by Hank Drake indicates, Piero Coppola was also grandfather of the famed film director Francis Ford Coppola. It's interesting to note that the latter's "Godfather" films are essentially grand operas of pride and revenge (especially III, where the climactic final scenes are actually set in an opera house during a performance of Mascagni's similarly-themed "Cavalleria Rusticana"). Piero's son Carmine Coppola was a film composer (e.g., a small part of the otherwise Rota-composed Godfather films, and a very Satie-esque, Gymnopedie-like film score for "The Black Stallion"). It's also worth noting that the Prokofiev 3rd can be heard as a prize-winning peformance in the delightful film "The Competition," starring Richard Dreyfuss and Amy Irving (the Prokofiev excerpts heard in the film were played by pianist Daniel Pollack).
I'm afraid I can't agree with Mr. Drake's characterization of this 3rd Concerto's performance as "definitive." There are just too many equally valid ways to perform a great work, none of which should be called the "one and only." Even when I feel that a reading is as close to definitive as possible (say, Richter's recording of the Prokofiev 5th Concerto), I am more inclined to say "best I've heard" or "finest known to me" or something along those lines, simply because I haven't heard them ALL.
The 3rd Piano Concerto has had no shortage of fine recordings. In fact, I was amazed to discover that the Philips CD series "Great Pianists of the 20th Century" contains no fewer than FIVE of them: Argerich, Gavrilov, Janis, Kapell and Katchen. Of those, I prefer the Kapell (with Dorati; Kapell also left a great "live" recording with Stokowski on M&A, but the sound is poor). Yes, I think this Prokofiev/Coppola account is a GREAT one, and I am happy to own it along with those two by William Kapell, the quirky version by Samson Francois (with Andre Cluytens on EMI), the fine collaboration of Alexander Uninsky with Willem von Otterloo (Epic LP), and a brilliant "live" account from Nikita Magaloff with conductor Lovro von Matacic (Disques Montaigne).
Prokofiev is especially remarkable here in the short solo pieces like "Visions fugitives," and his accounts are among my very favorites, along with those by Richter, Neuhaus and Katz.
Incidentally, Prokofiev also made a 1938 recording, this time as a CONDUCTOR, of badly-played selections from his own "Romeo & Juliet" with the Moscow Philharmonic (available on a Parnassus CD). Judging from that evidence, I won't hesitate to say that Prokofiev was DEFINITELY better as a composer/pianist than he was as a composer/conductor!
Is this Prokofiev 3rd Concerto a "definitive" recording? No, I don't believe there is such a thing. Is it a VERY GREAT recording that's a "must-hear?" Absolutely!