I know little about World Series press pins, but enough to ask some questions that might help you ID it. Do you have the other pin that you referenced, the one that has the word "Press" on the feather instead of "Braves?" A photo of it would suffice as well. I will bet it is different in more than just the Press/Braves distinction.
First, World Series press pins are issued before the WS. The winner of the series ("World Champions") can't be known before it is played. Second, even the crown is a bit ostentatious. Yes, they were "National League" champions, but by definition each team in the WS is a league champion. Third, WS press pins are very understated. They simply state the team name and usually "World Series" on it (or it might be implied by a globe design). Most are dated, but some are not. Some list the dates of past WS appearances. The Yankee press pins will typically list the number of times the team has been in the WS, like "It's our 30th." For the Milwaukee Braves in 1957 it might read "Our First" or counting their time in Boston "Our Third."
WS press pins are typically designed by high-end jewelers, like Balfour. They would not permit another party to make variations of their original die to produce souvenir pins to be sold to the public. My guess as to what you have here is the product of some vendor's attempt to sell a souvenir of the Braves 1957 championship. Pinback buttons are not expensive to make. I imagine the cost of having a die cast would be substantial. Is there any marking on the reverse as to who made it? It might have been made by the maker of the press pin, but I doubt it. It is an honor to the jeweler to be selected as the maker of a team's WS press pin. I don't think they would cheapen it by also creating a souvenir from the original die, but maybe. If it is the same company, then my guess is the players and major front office people got rings, and people holding less prominent positions got this pin.
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