What is the best way to evaluate GPS antenna performance by receiver data only?
None of your approaches are better than the simple "how well does my GPS receiver work for my application" test.

GPS antennas are actually combined antennas and amplifiers. So you'd not only have to take the property of the actual antenna (gain/directivity, efficiency) into consideration, but also (partly conflicting) properties of the amplifier (gain, noise figure, iiip3,...). That all makes testing the device actually application specific:

If you're using it in an urban environment, you might not want the amplifier to be too sensitive, because sensitive amps are usually faster at being driven into nonlinearity by interference, and there's a lot there.

On the other hand, you'd of course want to amplify even the weakest signal if you're traveling in a dense, wet mountain forest where satellite signals are heavily attenuated.