14 AWG can handle several thousand watts at HF no problem, assuming it is a straight wire and not coiled, and for antennas stranded wire can handle a little more power than non-stranded wire. If it is coiled how much power it can handle at a given frequency depends more on the coil design then the diameter of the wire. The larger coils with a larger spacing between the windings is more efficient then the smaller coils with wires right next to each other. Such designs can also handle more power simply becasue the windings of the coil are further apart, and thus it takes more of a voltage difference to arc from one to the other.
Power handling has little to nothing to do with antenna gain. Bandwidth, however, is indirectly related. With rare exception (very rare) the higher the bandwidth in the antenna system directly equates to higher losses, which lessens the amount of signal radiated from the antenna, thus lowering potential gain. That being said, I highly doubt you will notice much of a performance difference with the difference between those wire diameters in the real world. The difference is calculated by the ratio of the wire's diameter compared to the wavelength in question. With the wavelength at these frequencies being 36 feet give or take, there really isn't much of a difference as far as the RF signal is concerned...
I am curious how much power you plan on running?
And I agree with those from above, get the ARRL Antenna Book. There is a lot more regarding antennas in there than in the ARRL Handbook...
The DB