The FM transmitter with the short range will have a much farther range to a very sensitive FM radio in an expensive stereo or in a good car radio. Also the antennas must be good and aligned at the same angles.
The circuit has low output power because its supply voltage is very low, its oscillator provides a weak input to the output transistor and the 150k base resistor provides low base current.
You asked about using a darlington transistor to boost the output power. Then why didn't you look at a datasheet?
Here is the specs on the datasheet of a small darlington transistor. At 1kHz its minimum gain is 20,000 but it is only 1.5 at 100MHz over a narrow range of current. So its output power is almost the same as its input power and it is useless.