Chelsea were in a terrible financial place and would be going in to administration and become expelled from the football league pyramid without Roman taking over. Aside from a few good years prior to the takeover, they were also really really bad for almost 50 years. Chelsea were a consistent second division side in the 70s and 80s and were a smaller club than City with much less historical sucess and significance pre takeover. Before the sugardadies, City had 2 league titles pre takeover compared to Chelsea’s one, and a much much larger fanbase. City were a genuine football club who had the entire region of eastern Manchester supporting them. Anyone who lived in Manchester and didn’t support United went for City. Chelsea were like 7th most popular in London with low attendances and on the brink of liquitation in the 80s.
As far as buying sucess goes, Chelsea are by far the worst. Not only were they the first genuine oil club and the ones who started the trend, they also went to a larger exteme in spending ridiculous sums in comparison to City and PSG to build a solid foundation. Both City and PSG were also more sucessful and supported clubs than Chelsea pre takeover.