Giroud arrived as one of the club's marquee summer signings, given the unenviable task of replicating Robin van Persie's output, while the freshly contracted Theo Walcott's desire to adopt a more central berth is well documented.
With the Gunners generally employing one main striker, Arsene Wenger is often in a quandary about which of the two men to select in that role.
After a mini period of employing Walcott as the lone front man, Giroud has been back starting recent fixtures, with Walcott occupying his more familiar attacking berth on the right.
But what do this season's statistics reveal about the pair?
First off, here's a look at some shooting results to gauge how effective both men have been in front of goal.
These numbers shine more favourably on Walcott. He tests the goalkeeper more often, is much more clinical with his chances and has, of course, registered more goals at a better strike-rate.
Giroud reels off more shots of the two, but that can perhaps be attributed to the greater amount of time Walcott's lined up in a wider role—13 starts to six, according to WhoScored?.
It's the Frenchman who's been presented with far more clear-cut chances but has been considerably wayward with these more inviting openings.
He will be disappointed with just four goals from 20 here, a return Walcott trumps with eight fewer opportunities.
Quite simply, if Arsenal get a chance in and around the penalty area they want it to fall to Walcott. He possesses the superior finishing ability and has enjoyed a more consistent season in front of goal so far.
Next here's a look at some other essential contributions for strikers.
This is where one would expect there to be evidence of Giroud's more rounded game, but once again, it's Walcott who appears the more productive throughout.
Predictably, Walcott's a far more penetrative dribbler, and Arsenal have been marginally more successful with him in the team.
He's also significantly more accurate with his passing—some 20 percent—and a colossal 27 percent more in the final third.
Giroud's passing numbers are quite alarming. Of players with at least 250 passes this season, his accuracy is the fifth worst in the Premier League (excluding goalkeepers) and the third worst of players with over 500 passes.
Some of that may be linked to the Frenchman's "dispossessed" and "loss of possession" stats which are also quite poor and in need of improving.
Giroud does prosper is in the air, where he wins 56 percent of aerial duels, an impressive ratio for a front man. However, given his poor ball retention stats, it suggests Arsenal are targeting him for quick attacking territory and, although he may win the initial header, his hold-up play is letting them down.
An argument for his inclusion perhaps centres around his "touches" stat. He is slightly more involved than Walcott, although the Englishman's numbers are augmented by his more regular outings on the flank.
For example, in recent games as a wide attacker, Walcott recorded 62 and 52 touches, but just 18 and 23 in two previous outings as a striker.
This shows he can be isolated as a striker, especially as Giroud emerged from the bench in those games and almost surpassed his total in just 30 minutes.
Clearly, Walcott is the more productive goalscoring option for Arsenal. Given the opportunities he's had, Giroud may be disappointed not to have registered a few more strikes by now and needs to refine certain areas of his game.
Based on these results, there are certainly more games Walcott should be playing through the middle, preferably against less physical sides, where Arsenal can also adopt a higher line to reduce the distance between him and the midfield.
Overall, the Gunners need to find ways of ensuring it's Walcott who's at the end of the bulk of their attacks. While that would be simpler with him up front, it doesn't necessarily mean he needs to play there all the time.
There are several understandable reasons for Wenger being reluctant to make a more permanent switch.
With Giroud on the pitch, Arsenal have more flexibility. They can sweep through teams, attack with more width or ask their front man to hold the ball up and play in some runners—although, as highlighted, the control in his hold-up play has been inconsistent and needs improving.
Another factor is that removing Walcott from the right, in place of Giroud, and then bringing in another right-sided midfielder weakens the overall quality more than with both players on the team sheet.
Even playing on the right, Walcott still crops up in several attacking channels and it seems he can get isolated and disconnected from the team if playing up front on his own.
Therefore, against the more physical defences, it makes much more sense to play Giroud. If he could brush up on his hold-up play, his passing and tuck away a few more goals, he would have a much stronger argument for a continued inclusion.
As it is, purely based on statistics, Walcott's the more reliable goalscorer of the two in and around the penalty area. In the right circumstances, he needs to be more regularly unleashed up front.
Statistics via EPL Index