As horrible as they are, I think Chelsea have always had a sort of weird blundering quality. City had a bit of that in the first few years under Sheikh Mansour, before they decided to settle into Guardiola and the idea of discovering a philosophy. Chelsea always feel as equally close to disaster as they do to glory. Maybe there's something more endearing about that than the coldness of City.
The difference for me, I feel, is that Chelsea were always a horrible club with horrible fans. When they sold out to a Russian thief (who purloined his ill-gotten gain by taking advantage of ordinary people), it felt like arseholes being led by criminals. They were already pretty iffy, this just confirmed it.
City though, that is a political game being played by petty demagogues, intent on using the popularity of a sport enjoyed by millions across the globe to distract from their own criminal activities occurring on a grand scale. Abramovich was a gangster spending his money on something he loved (and has been blacklisted by the Home Office for his raising his profile in this way). The Man City takeover was cynical statecraft that has seen more pressure exerted at the highest levels in government and the media than the Russian could ever hope to achieve. CIty have contravened UEFA laws and even intervened in the courts to ensure their project was not derailed, to the point of gaining control over the committee set to judge their infringements. Their behaviour is a whole new level of awful, at a club with a reputation for famously being much more likable than their city rivals.