P.S. From what I saw of polo in Argentina, your characterization is slightly off. There is a whole bunch of money going into polo now; the amateurs are mostly window dressing to support the pros.
As Tom says, there is no possible comparison.
Amateur Polo is a lot more expensive than amateur golf. An amateur playing top level polo these days can expect to spend well over $1 million in fees to the pros playing along side him for maybe a month in one of the top handicap tournaments. This does not even start considering costs of his own horse operation.
I would argue that outside Argentina, top amateur polo is a sport for those that have more than $100 million in the bank. This means top amateur polo is played by 0 or 1 goal players that can pay for pros and their horses, the equivallent of a 25 handicap golfers that can pay for Spieth, Rory et all to play for their team. Amateur golf is a ton more democratic.
Ironically, professional polo is only played alongside amateurs. That is, when pros are paid to play and win. 1 amateur per team (the sponsor or Patron) and 3 pros.
By contrast, the 3 most important tournaments in the world, are played by the top pros (4 pros per team), but it remains "amateur". No prize money at all and they do not get paid to play. And no amateurs can play in this.