As you apparently do a lot of work with antenna calibration, did you compare the results of both methods?
Yes, my recommended calibration procedure is not a perfect method, especially the "open" is obvious that it adds a reactive error, but most of that effect is taken care of by calibration and it is so far best found practical method. For checking amount of error do I typically use a resistor 10 kOhm as load and compare what the VNA measure. As stray-capacitance and inductive losses is expected to be same as for the short and 50 Ohm calibration-resistor can I pretty good see if reactive load measure correct enough. As I often design antennas with that kind of a few kOhm as impedance must calculating of a matching network be based on very correct values.
Doing calibration with a calibration kit, and mechanical compensate for thin coaxial cables length do work ok but in GHz-range and with intention to design a good T or PI matching network for a wide band antenna can a few degrees measurement error in smith-chart be difference between success and failure.
Making a impedance correcting PI network a bit beyond "fine-tuning" in GHz-range, requires that calibration must be very good if theoretical calculated correcting network and final measured smith-diagram should have any similarities. I do mostly succeed with that kind of network in first try now, but it did take me long time to learn how.