I know one thing that can make that sort of difference is fuel delivery. The FJR doesn't exactly have a long fuel line, so it doesn't take much for the pump to get fuel pressurized and flowing out the injectors. On a car with the pump way back in the tank, it can take a while to build up enough pressure to get fuel squirting...
Additionally, there are some other design considerations that affect this. Many cars use an oil pressure safety switch, with no oil pressure, the fuel pump won't kick on. Some models use a relay to 'bypass' this mode when the car is starting, while others may actually not turn the pump on until the engine has built up 'enough' (read a couple PSI) oil pressure to satisfy the sensor.