If both the sine and square have the same total power, then the square wave will have less power at the fundamental and each harmonic frequency and assuming that we are talking only free space propagation, each component (fundamental or harmonic) will travel a shorter distance. So the sine wins.
As for the second question... The total power of a square wave is twice that of the sine wave with the same peak amplitude, or +3 dB. However, the first harmonic of a square wave is down -4dB from the total power, so the first harmonic of the square wave is -1 dB lower than the sine wave. Also, the loop stick antenna is relatively high Q and has selectivity, so higher harmonics will probably not be well radiated. Considering these factors, the sine wave wins again.