A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense. 

This is because 

 1. You already know for certain that the model is gonna be wrong.
 2. The residuals that you end up with have no relation with the hypothesised distribution of errors that you use to test different hypotheses. (you do not have a statistical/probabilisitc model)
 3. Your goal is not to test a hypothesis, but to characterize the prediction performance of a simplified model.

----

Most often people describe models in terms of the percent of error for predictions.

Examples:

- [*Sludge pipe flow pressure drop prediction using composite power-law friction factor-Reynolds number correlations based on different non-Newtonian Reynolds numbers*](http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S1816-79502012000400017)
> It is shown that these correlations can be used to predict pressure
> drop to within ±20% for a given sludge concentration and operating
> condition.
 
- [*Predicting the effective viscosity of nanofluids based on the rheology of suspensions of solid particles*](https://doi.org/10.1016/j.jksus.2017.09.016)
> The present model suits with the 501 viscosity values with mean
> deviations lower than 5% and 75% of them are within the correlation
> coefficient 0.78–1.
> 

- [*Application of artificial intelligence to modelling asphalt –rubber viscosity*](https://doi.org/10.1080/10298436.2014.893316)
> Figure 2 presents a comparison between measured viscosity ($\rho$) and
> the viscosity calculated by Einstein model. A difference between
> calculated and measured values confirms that there is an elevated
> physical interaction between asphalt base and rubber particles.


- [*Bond contribution method for estimating henry's law constants*](https://doi.org/10.1002/etc.5620101007)
> A correlation coefficient (r2) of 0.94 was determined for the
> relationship between known LWAPCs (log water‐to‐air partition
> coefficients) and bond estimated LWAPCs for the 345 compound data set.


Basically you can google any model that is a simplification of reality and you will find people describing their discrepancy with reality in terms of correlation coefficients, or percent of variation.