VAM & W/kg estimates
The plot compares the W/kg estimates for each of three gradients: 6%, 8% and 10% for a range of VAMs between ~800 m/h and ~2000 m/h. A red unity line is included for reference.
To make the variances between each method a little easier to see, the following chart plots the difference between the two W/kg estimates, again a line for each of the three gradients: 6%, 8% and 10%.
I don't have a lot to add to the charts other than to say the Dr Ferrari formula is a bit of a quick and dirty way to estimate W/kg from ascent rates but it does not consider a range of variables included in the Martin et al formula.
In particular we can see the estimates can vary quite a bit depending on both gradient and on VAM.
Same plot as above but this time with the variance expressed as a percentage of the Martin et al method estimate:
I would certainly place more faith in the Martin et al method, and that was also the conclusion of this paper by @ammattipyoraily and @veloclinic (Dr. Mike Puchowicz) which examined the different methods of calculation compared with actual power meter data from a large number of data files.
For consistency with the analysis in the paper above I chose rider mass and CdA in the middle of the range from that paper. I do not know what Crr assumption were used though. I settled on 0.005.
A Crr value in the range 0.004 to 0.005 would be typical and the impact on calculations of a difference between 0.004 and 0.005 is equivalent to adding 0.1% to gradient (and an associated bias error in W/kg estimates of about the same order).