Based on personal opinion, it's Laszlo Papp, based on facts, IT'S LASZLO PAPP!
Why? Fact is that Papp competed in the era that amateur boxers fought exactly like professionals, no headgear, small gloves, the only difference was that they fought less rounds, but Papp was that good that floored or KO'd them inside 3 rounds, he did not need 15 like Sugar Ray Robinson for example, that good Papp was :) Now the other 5 legends who make my top 6 of all time in amateurs, Teofilo, Felix Savon, Boris Lagutin, Sergei Kulej and Oleg Saitov, even though technically, specially in the cases of Saitov and Lagutin might were superior to Mr. Papp, they simly did not achieve the "undefeated" status of Papp in the big international competitions. Mr Papp, won in all 3 Olympic games he took part in, he won in both European championships he took part in and he won in all 17 tournaments which were officially ranked by World Amateur Boxing Organization (before AIBA) . If there were AIBA world championships back then , there is no doubt Mr Papp would have won 5-6 of them too, i mean the man was the best, it's undeniable. Also Mr. Papp has the best record of all the rest gentlemen, he has the most wins (over 300 officially, almost 500 unofficially), the less losses (only 3 officially and 2 unofficially) , the most KO's by any amateur , the most first round KO's by any boxer in history and the only from that group of 6 legends, who won medals in 2 different weight divisions. By any way you look at it Papp is superior P4P to all of them.
He also became the first man ever to win 3 gold medals in 3 different Olympics and he said he made a big mistake turning pro, since he would have won a 4th medal if he stayed as an amateur, a record that could hardly ever break in Olympic boxing.
Also Papp even though way past his prime, he turned a professional, the only of this elite 6 group and he won the European title and he was one breathe away to become a world champion too, before the communist government of Hungary would not allow him to compete for the title. He stayed undefeated as a professional as well.
Papp also if i am not mistaken is the only of the 6 who was inducted into the International Boxing Hall Of Fame in 2001. In 1989 WBC President Jose Sulaiman gave Papp an award for 'Best amateur and professional boxer of all time' and granted him honorary champion status of the World Boxing Council.
As a youngster Papp had to grow in the middle of the Second World War. When the war was over, Papp started to get interested in sports. At first he played soccer like so many other Hungarian boys, but after seeing a boxing movie called “The Final Round” all that changed and the young Laszlo picked up a sport that would make him a legend. Few could have guessed at the time what this young boy who had been enchanted by the movie would yet achieve. He started boxing at the age of 17, pretty old and in a country that knew nothing about boxing at the time and still managed to become the greatest boxer of all time period. Imagine if he was born in America which was obsessed with boxing at the moment and the man could enjoy all the facilities USA would offer him.
Most of all, Papp was known as a quiet, honest man who never bragged about himself but did his talking inside the ring. And in there, his fists told a story that will never be forgotten from the minds of the boxing fans.
Rest in peace legend!
PS
Funny how some people name Teofilo Stevenson the best over Papp, when Teofilo himself said that he would need 2 lifetimes to achieve all Papp achieved with the poor facilities Hungary had to offer to Mr. papp at the time. Teofilo was born in the country that you either make cigars or become a boxer and still achieved less than Papp.