Realistically Arsenal are never going to compete with the Manchester clubs or Chelsea to sign the very best players because they just don't have the finances. Wenger already worked that out years ago which is why he doesn't pursue them.
The club has developed well in the last ten years though. They have a bigger international following than they've ever had, they have an amazing new stadium (and they're already considering ways to expand it), profits are good, league performances are consistently good.
It's been a while since the days of Bergkamp and Henry but hey, look at Liverpool - it wasn't long ago that they had Xabi Alonso, Mascherano, Arbeloa, Torres when he was actually good, etc. Now look at them. And has changing managers every 18 months helped them improve their league performances?
They used to be the biggest club in England. For a couple of decades. That's just how it goes.