Hi MG, The F-ratio approach is only valid for comparing linear models that are nested. Because your models are neither linear nor nested, there's no good reason to think this will work well.

I think the most common thing to do in a situation like this would be to compare the models' information criterion statistics, such as AIC or BIC, and pick the model that has the lower value -- but note that this is technically a bit different from comparing the two models on which has the higher value. So this may or may not work for you, based on how committed you are to using as the basis for comparison, or if you just want to know more generally/vaguely which model is more "consistent with the data."

What I personally would probably do here is use a bootstrap approach. In each iteration, sample the rows of the dataset with replacement, fit both models to the resampled data, compute their values, and then take their difference. Do this enough times and you'll have a bootstrap sampling distribution of the difference in values. Now check to see where the null value of 0 lies in this distribution.