As Wenger and Mowbray prepare for Wednesdays Champions League qualifier second leg tie, both mangers will have much to consider.
For Wenger the big question will be who to rest ahead of the weekend's league match, against champions Manchester United.
An early season result against one of the serious title contenders, and fellow member of the EPL's "Big Four," would be an important result. With a two away goal advantage over Celtic, Wenger might therefore be tempted to put out a weaker side on Wednesday.
Manchester United play a high paced, direct style of football, that relies heavily on stamina. This has often been the reason for their ability to snatch injury time winners.
With United not playing a midweek match, Wenger may well decide to rest key players, with this in mind. However a run out might provide the opportunity for some to find match sharpness, that is often lacking this early in the season.
Playing on the big stage of the Champions League is vital for a club of Arsenal's ambition though. When you add to that the revenue generated by qualification, especially considering the club's current financial constraints, they dare not risk failing to qualify.
Looking back to the first leg tie against Celtic, Arsenal were certainly fortunate to get the result they did. The two away goals coming from a lucky deflection and an unfortunate own goal.
While they were worthy winners, Arsenal's attacking flair was stifled by Celtic's defensive endeavour. Celtic managed to carve out their own chances, their best two falling to Scott Brown, who disappointed on the night.
Based on their 5-2 rout of St Johnstone, at the weekend, they can certainly find the back of the net. In that match, new signing Fortune opened his account for Celtic, contributing two goals for the Hoops. After the match he said "I can't wait until Wednesday."
As a pragmatic manager, Wenger will probably not make too many changes to the line-up. Keeping experienced players in the side, rather than risk missing out on qualification. It's likely he will also want the team to play a slower paced game, emphasising defensive safety.
This would also be an ideal opportunity to give a few of the younger young guns a chance to shine. With Fabregas ruled out, this may be Ramsey's chance to take to the European stage. If the first half goes to plan, I would expect to see early substitutions in the second, with hopefully more chances going to the youngsters.
Tony Mowbray's own conundrum is somewhat more straight forward. To take the game to Arsenal or play it safer to avoid a humiliating result.
While at first you might think that Celtic have nothing to lose, Mowbray certainly does. He will have seen Arsenal's recent demonstrations of their ability to ruthlessly punish teams. A more attacking attitude in Wednesday's match, from the Bohys, may leave them too exposed to this.
He may well be wonder whether an overwhelming scoreline against his team might unsettle his board's faith in him, this early in tenure. However, he will also need to show that his ambition matches his clubs.
His comments regarding the forthcoming fixture, indicated this may be in his thoughts, when he said "I understand that if we lose 2-0 again, I will be judged to have got the team wrong again but if we win 3-0 then hopefully everyone will be pretty happy."
Celtic showed against Dinamo Moscow, in the previous qualification round, that they can overhaul a home defeat in Europe. Dinamo certainly do not have Arsenal's quality though, and the goal difference is double.
An energetic start from Celtic may well be on the cards. As an early goal, in their favour, would make a big difference. Higher commitment to attacking would be unlikely to be sustained, as Arsenal can be very effective on the counter, and judging by the second half of the last leg, they are the team with greater stamina.
Ultimately, how Mowbray and Celtic approach the game, will be influenced by the noises coming from the board. Their negativity or positivity directly reflecting the boards attitude toward the tie.
As club that has a lot of pride, I would hope that they endeavor to make a fight back. That pride might alternatively be the reason they play it safe.
Like any football fan, I hope that it will be a good open game. Experience tells me that it's more likely to be a more cagey affair.