How can you assert that a fit with one model is lesser fit than a fit with another model? Define 'lesser'?
The best fit is when you have a better R-squared value than any other fits. Excel calculates the best fits for every model automatically, so you can just conclude that a log-linear model has a better fit (0.94) than log-logistic (0.73).
If I am not mistaken, the best R-squared (least error from the data points) would be an N-degree polynomial for N data points such that the curve passes through every point.
Thus 'best fit' may have no correlation to predictive power.
Surely you of all people understand the concept of overfit, as it is deeply connected to ergodicity, which seems to be central to much of your thinking.
If you want a pragmatically useful and statistically rigorous treatment of overfit in predictive financial models, I suggest recent works of Marcos Lopez de Prado.
For my purposes trivial heuristics in the number of parameters are often more practical, since I need to do calculations for very large ensembles of diverse models,
but Lopez de Prado's stuff is on much firmer epistemic ground and very suitable to systems involving relatively small numbers of models (perhaps millions).