The 22-year-old stars will go head-to-head when Brazil plays Colombia on Friday, when only one will get the chance to continue his run at the tournament.
Wearing the No. 10 jerseys, both have lived up to expectations so far, enough to be included in discussions about the tournament's best players along with established stars such as Lionel Messi and Arjen Robben.
Neymar has been decisive for Brazil, scoring four goals in four matches. Rodriguez has been crucial for Colombia with his tournament-leading five goals and creativity in attack.
''I already knew that James was a great player,'' Neymar said. ''And now he has been showing his talent at the World Cup.''
Rodriguez has been one of the tournament's sensations so far and has helped Colombia get over the absence of star striker Radamel Falcao, who missed the tournament because of a knee injury.
It didn't take long for Rodriguez to become the focal point of a Colombia team that won all of its four matches seemingly without any real difficulty.
''It's not easy to achieve what I've done, but my view is that when you have a dream and you really pursue it and picture things like this happening, then it can become a reality,'' Rodriguez told FIFA.com. ''If you want something and you work hard for it, then it can happen.''
The Monaco player scored in each match, including two against Uruguay in the second round, and has been voted player of the match three times. One of the goals against Uruguay is already considered one of the best of the tournament so far. He chested the ball and quickly turned to fire a powerful shot over the goalkeeper from the top of the penalty area.
Rodriguez had already scored a stunning goal against Japan in the group stage, flicking the ball over the goalkeeper after getting past a defender with a nifty move inside the box.
''James is outstanding despite also being young,'' Neymar said. ''He has been showing that he is a great player and needs to be congratulated for the tournament that he has been having. But I hope his run ends now and that Brazil advances.''
The Brazilian forward came to the tournament amid a lot more hype than Rodriguez, already knowing that he was carrying the responsibility of leading his team to the title on home soil.
Neymar scored twice in the difficult 3-1 opening win over Croatia, then added two more in the 4-1 rout of Cameroon in the group stage. The Barcelona star also showed his cool by calmly converting his penalty in the tense shootout against Chile in the second round.
''I don't know who will play better, I just hope that Brazil comes out on top,'' Neymar said, referring to his duel with Rodriguez. ''I've already said before the World Cup started that I don't care about being the best player or the top scorer, all I want is to win the title. If I don't play well but Brazil wins, I'll still be happy.''
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