Manchester City's tradition is not as strong, but has currently built a very strong team, with players like Tévez, Agüero, Silva, Kompany and the Italian coach Roberto Mancini, a coach with strong records, a strong personality and who used to be as well a very fine technical player.
Chelsea is a combination of both, with stronger tradition than City, has won more prizes won, and remarkable names as Drogba, Čech, Lampard, Terry, etc... that are known to every fan, and have achieved the status of World Class as well.
Both last clubs can offer a much higher salary, but their future depend on the finances of their owners. What if Abramovich (Chelsea) or the Abu Dhabi United Group (Manchester City) to lower the priority of football and decide to stop spending money in the clubs? What if the Financial Fair Play sets in soon, and the clubs are not able to buy any player they want anymore to keep themselves in the top 3? Then it all comes back how well the clubs are led, and what the trainer can do to stay ahead.