This answer mentions that the J-2 engines used by the Saturn V's second and third stages were substantially more resilient than the "extremely complex and sensitive" Space Shuttle main engines. What led to the difference between the two engines? Was it just the nature of going from a gas generator cycle to staged combustion?
A number of factors contributed to the complexity. Staged combustion was definitely a big one. The SSME also ran at a much higher chamber pressure than the J-2, 3000 psi vs 760 psi. This seems to have required two turbopumps for each of the propellants instead of the usual one -- there are low- and high-pressure turbopumps for the fuel (LPFTP, HPFTP) and low- and high-pressure turbopumps for the oxidizer (LPOTP, HPOTP). Since turbopumps are one of the biggest sources of headaches in large engines, doubling their number had a predictable effect on maintenance.