This sounds like a competition or sport. You can enjoy the advantage of you are in the lead, or the other team has a player sent off, or you go into the second leg with an away goal.
You take the advantage by capitalising on it. If the opponents get their goalkeeper sent off, and he's a really good goalkeeper, and his replacement is one of the defenders, you should take the advantage. Make the most of it. Exploit their weakness or vulnerability. Or maybe your pawn in chess has become a queen, and now you have two queens. You can take the advantage and corner the king. Use them to take out their queen.
They can both mean to use the advantage. You are in a good position and you should take action.