>>14217866FFSC is the most benign of the staged combustion cycles. It's also the most complex, and since oldspace is scared of using additional tubropumps they poo-poo the combustion cycle design.
>>14217877ORSC uses a denser gas in the turbine (because it's oxygen rich) which allows those turbines to be more compact. FRSC doesn't involve handling hot oxygen rich gas. FFSC offers more manageable turbine conditions at a given main chamber pressure than either ORSC or FRSC due to having more less flow through each individual preburner (though more preburner flow once you combine the two).
The ranking in my opinion goes FRSC to ORSC to FFSC.
Fuel rich staged combustion is metallurgically easier but you need a bigger turbine because you're producing a lower density hot gas to drive it. This is especially bad for hydrolox btw, an ORSC hydrolox engine of the same size would out-perform the FRSC RS-25 engine. FFSC is the best in terms of achievable chamber pressure, TWR, and Isp, and it's also the best in terms of building a reusable rocket.
Elon said Raptor is having trouble with heat in the main combustion chamber. The combustion cycle has nothing to do with this, it could be ORSC or FRSC or even GG, the issue is that at the chamber pressures they're hitting, heat flow into the nozzle is extremely high, so they need a very fine tuned coolant flow path design to handle it. IF the issue were the FFSC combustion cycle, he would have said they were having turbopump problems.
