At one point we were very competitive in the Champions League, and Wenger did a great job to put us up to that level. Unfortunately, for the past 2-3 years, we have fallen off significantly and haven't been able to compete at that same level. Case in point, not many fans have hopes of us beating Bayern. Go back 3-4 years, we would be level on favourites to win. To remain elite, you need to match it with your performances. We haven't done that for quite some years....
Seeing as we actually feed the elites you mention, I would put us slightly ahead of Chelski & the dippers.
In terms of football generated revenue and club infrastructure we are up there. I wouldn't include Chelski who would be nothing without the Russian gangster.