"Although they beat us the last time we played, I don't see either team having a clear advantage," he said.
"This a new phase: both teams have advanced to the second round and are on equal footing."
Mexico qualified for the second stage with two wins and a draw, beating Croatia
1-0 and Ecuador 2-1 before giving up a late goal against Italy.
The US meanwhile survived Group D with a superb opening 3-1 win against Portugal, a 1-1 draw with co-hosts South Korea and a disappointing 3-1 defeat to Poland.
Aguire said: "The Americans will come out strong. Now that neither team is playing for points but for goals, it will be a very hard-fought match.
"Mexico will have to continue doing what it has done so far in the tournament: control the ball, distribute it well, basically play our game."