Which is more fuel efficient?

With modern fuel injection systems car engines can get the precise amount of fuel that they need. The amount of fuel injected depends on the readings on a variety of sensors including the Manifold Absolute Pressure (MAP) sensor.

If you are going downhill and you keep the transmission in gear causing the engine to rev higher than idle but also causing a lower than normal absolute pressure in the intake manifold, would you use less fuel than if you put the transmission in neutral and coasted with the engine idling?

It seems to me that the ECU should be able to recognize that you are “engine braking” and cut off the fuel, or at least use a lot less fuel than idle.

many cars actually do employ deceleration fuel cut-off (DFCO.)

Make that most if not all cars. Even ones that don’t have MAP sensors.
The ECM knows engine RPM and throttle position, that is all that is needed.
And before anyone objects, yes the fuel gets turned back on before the car stalls.

I always thought that the Throttle Position Sensor was only used for shift points. What else is it used for?

Lots of stuff.
It backs up the input from the Mass Air Flow sensor /Manifold Absolute Pressure sensor to determine engine load and abrupt changes. Lose the MAF/MAP the ECM uses the TPS instead.
It detects idle position. Some functions are only allowed at idle. For example when the engine is cold, the ECM will retard the timing at idle to get the engine to warm up faster. If the engine is in danger of overheating, the ECM will advance the timing at idle to bring the coolant temp down.
It detects Wide Open Throttle for full throttle enrichment, and AC cut out at WOT.
ETA it supplies info to the electronic automatic transmission to make the trans shift smoothly.

and now the TPS is a redundant check for throttle-by-wire systems.

It was late, I forgot that.
Yes the TPS is an important input on fly by wire systems.
On Volvo they use:
Two accelerator pedal sensors (one analog, one digital) to determine driver input
Two Throttle position sensors (which read opposite from each other)to determine actual throttle position
Two brake inputs, the brake light switch and a brake pedal position sensor.
If any of the six fail, various fail safe programs come into play including brake override where if the brake pedal and accelerator pedal are both depressed, the brake overrides the throttle input.

Are data from the Throttle Position Sensor compiled in the TPS report?