Not really. Historically City were obviously a bigger club than Chelsea if you look at trophy count. By the 1980s we were fairly comparable, both of us yo-yo'd up and down between Div 1 and Div 2. We then both got promoted together in 1988/89 and for the next few seasons up until the end of 1992/1993, City finished above Chelsea 3 times. I mention 1993 as a watershed moment because that's when Matthew Harding invested a considerable sum of money into Chelsea (which certainly helped the club to be able to afford the likes of Zola, Gullit, Desailly, etc. over the next few years). Chelsea's fortunes really started to improve, particularly from 1996 onwards, and they won a number of cup competitions while we tumbled down to Div 2 (by then the 3rd tier). Chelsea then got their next bump via Roman in 2003, while we got our bump a few years later in 2008.
I take your point on the difference between rich individuals and rich countries. Chelsea's two rich individuals helped them become more successful (or bigger if you prefer) than City over essentially a 15-year period in the respective clubs' histories, between the mid 1990s and the end of the 2000s.
