The biggest question I have is whether Giroud and Podolski are replacements for van Persie, or for Park/Bendtner/Vela/Chamakh. If RvP is replaced by a very promising talent; like Yarmolenko, Leandro Damiao, van Wolfswinkel or Destro, then there is a hope the team can challenge. If he is replaced with a proven top striker, like Huntelaar, Llorente or Jovetic, then I fully believe we'll challenge (if a DM is added...).
All the big players Arsenal have lost have been foreign born with ambitions to play for the big continental clubs (Anelka, Vieira, Henry, Fabregas). Who wouldn't want to live in Barcelona? Who wouldn't want to be PAID to live in Barcelona?! Nasri is perhaps the exception (Hleb, Flamini, Petit and Overmars were probably influenced by lifestyle and money). But we've seen what type of man he is (I think Clichy was allowed to go as Wenger ultimately thought Gibbs would be better, and Toure/Adebayor left due to disagreements with key players). I'm not regretting that Nasri and the other ex-Arsenal players at Man City left us. Van Persie; you can see and understand his dilemma. But he shouldn't have said those things in his statement, nor to his Dutch pal before Euro 2012. And if he goes to Man City, that one would hurt.
The case studies that will determine Arsenal's standing, ambition and influence will be Walcott's contract decision, and the futures of Wilshere, Chamberlain, Gibbs and to a certain extent, Szczesny. I can see foreign players like Sagna, Vermaelen and Koscielny wanting to play in another country. But what will our British talent (Szcszesny is practically a Cockney) do?