Both Walcott and Giroud have been rotated this term, depending on the opposition, and it was the Frenchman who was preferred against Dinamo Zagreb in the Champions League last week, days after the ex-Southampton youngster was selected against Stoke City.
It was the jet-heeled Walcott who was chosen over Giroud in Saturday's defeat to Chelsea, and the 26-year-old has had a number of people calling for him to finally be given an extended run as a centre-forward.
The injury to Danny Welbeck and the subsequent refusal to sign another striker means Walcott and Giroud are the only recognised centre-forwards at the club, and while Alexis Sanchez can operate in the position, Wenger is expected to rotate the pair on a seemingly weekly basis.
Both players offer different things to how Wenger wants his team to play, with Walcott's electric pace able to stretch teams and allow the wealth of attacking midfielders to flourish with the space afforded to them by the hard running of the striker.
Wenger has the likes of Mesut Ozil, Santi Cazorla, Sanchez, Alex Oxlade-Chamberlain and eventually Jack Wilshere able to operate high up the field and make the most of runs made by the pacy Walcott.
In contrast, target-man Giroud is able to bring his teammates into play closer to him with his strength and ability to hold the ball up with his touch and technique, and the differences between the France international and teammate Walcott are something Wenger is acutely aware of.
In fact, their respective differences are why the Frenchman has refused to choose one as his definitive No.9 this term.
Wenger told reporters ahead of his visit to North-London rivals Tottenham in the League Cup on Wednesday, as covered by the Daily Mirror: "With Olivier Giroud, it is a competition with Walcott. When one plays people always ask, 'Why did you not play the other one?'
"When you have two top-level strikers, some games Giroud plays and some games Walcott plays. What we want to do is make the right decision for the right game.
"For two guys it can be interesting for the squad as they both have different qualities. They complement each other very well. Giroud's all-round game is vital because it is one of his assets. He can protect the ball, he can hold the ball, he can bring other plays in."