Does spread in error reflect spread in coefficient values when coefficients are dimensional and have different units?

I have two very different empirical models that estimate a quantity $$Z$$ from two quantities ($$x$$ and $$y$$). Lets call the two models (highly non linear) $$F_1$$ and $$F_2$$

$$Z = a_1F_1(x,y)$$

$$Z = a_2F_2(x,y)$$

I trained the model coefficient $$a$$ over a first dataset (cross-validation) and I am testing on a separate dataset. Model F1 gives smaller absolute error than the other, and also smaller RMSD (root mean square deviation). If I try to overfit $$a$$ to each realization of Z, the standard deviation of the overfitted $$a_1$$ is also smaller than for the overfitted $$a_2$$. To me, that indicates that the process is better described by F1 cause the same coefficient works great for all cases. However, I wonder if I am right to compare the spread (Standard deviation) of coefficients with different units? Should I use some dimensionless quantity such as the Coefficient of Variation (CV)? I see in the Wiki example that has problems when comparing the spread of Celsius versus Faranheit (different units) so I a bit wary. Which is the best option?