> Since (R_rad + R_loss) << X, the optimal R_load is approximately |X|, a value in the range of hundreds of Ohms for both a dipole and a loop.
Both small loop antenna and small dipole antenna, if built efficiently are of very high Q. That means a narrow band matching circuit in case of efficient power transfer.
> Nevertheless, some sources , suggest that the input impedance of an amplifier connected to a small loop must be as low as possible
If the loading impedance is high, the loop starts acting as a dipole, which distorts the figure eight vertical radiation pattern and decreases immunity to a near E-field.
> other sources  report success with a small loop and a common collector amplifier (the input impedance is hundreds of Ohms),
Depends on what do you want to optimize. I recommend reading the following article from Chevdar LZ1AQ (thanks, Chevdar):
I recommmend to read all his technical articles anyway. It is a great source of technical and theoretic information on loops.
Basically, the higher the load impedance, the better the SNR, but the higher the lower frequency threshold, worse radiation diagram and more sensitive to E-field. The null depths and low sensitivity to E-field are the reason to install the loop antenna in city environment, therefore keeping the load resistance low is important.
> and finally it is recommended to use a short dipole with a high
input impedance amplifier .
That is a completely different kind of animal altogether. Chevdar's active antenna amplifier could be switched to magnetic or electric field mode. He comments, that in the E-field mode the antenna has a better SNR in a rural environment, but is more sensitive to close e-field noise than the mag loop mode.
> The loss of the received signal power could be huge due to the load impedance mismatch.
Chevdar compares SNR of a tuned loop against an untuned loop. The SNR of a tuned loop is better indeed because of conjugate matching. The noise of a tuned loop is mainly caused by the thermal noise of the loop resistance. The noise of an untuned loop caused mainly by the thermal noise of the load resistance.
73, Vojtech OK1IAK, AB2ZA