It's a very complex topic, with no 'right' answer I don't believe.
In very basic terms, the lower the throttle the shorter the injection pulsewidth (i.e. the injectors are open for less time, and hence inject less fuel given fixed fuel pressure and flow rates). The lower the RPM the lower the pulsewidth as well.
Conversely, higher throttles and RPMs increase the pulsewidth.
Injector pulsewidth peaks at peak torque (or it should in ideal conditions - obviously with the complex nature of an engine it might be that this isn't exactly the case), but because the engine is spinning faster it's injector more frequently. So peak fuel flow is at peak RPM.
Ultimately, the question is which is better - accelerating from 1500rpm to 3000rpm using around 30% throttle for 50 seconds OR accelerating from 2500 to 4000rpm using 70% throttle for 20 seconds and then cruise at 2000rpm for the remaining 30 seconds. Assume that the road speeds in each test are the same (i.e. different gears).
Personally I believe that the latter is more efficient, and hence in your example the manual mode in a lower gear with more throttle will give better mileage than the auto mode choosing a higher gear.
I could give you the fuelling map of my race car (which I know isn't as complicating or refined as a road car map that will have spent weeks being developed on a dyno and on the road), and you can use that to work out various possibilities...
In very basic terms, the lower the throttle the shorter the injection pulsewidth (i.e. the injectors are open for less time, and hence inject less fuel given fixed fuel pressure and flow rates). The lower the RPM the lower the pulsewidth as well.
Conversely, higher throttles and RPMs increase the pulsewidth.
Injector pulsewidth peaks at peak torque (or it should in ideal conditions - obviously with the complex nature of an engine it might be that this isn't exactly the case), but because the engine is spinning faster it's injector more frequently. So peak fuel flow is at peak RPM.
Ultimately, the question is which is better - accelerating from 1500rpm to 3000rpm using around 30% throttle for 50 seconds OR accelerating from 2500 to 4000rpm using 70% throttle for 20 seconds and then cruise at 2000rpm for the remaining 30 seconds. Assume that the road speeds in each test are the same (i.e. different gears).
Personally I believe that the latter is more efficient, and hence in your example the manual mode in a lower gear with more throttle will give better mileage than the auto mode choosing a higher gear.
I could give you the fuelling map of my race car (which I know isn't as complicating or refined as a road car map that will have spent weeks being developed on a dyno and on the road), and you can use that to work out various possibilities...