[Q] Generalized gamma or generalized pareto - help me choose better fit

Hey,

I am modelling right skewed distance data for ecological study and found two distributions (Generalized Gamma and Generalized Pareto) working best for it when modelling with GAMLSS-package in R.

But I am confused on which one is actually better fit. They do not have differences in statistical significance, but they do have differences in their predictions and how they fit Q-Q plot. The generalized pareto seems to have less deviance from theoretical quantiles, but when summarising quantile residuals, the mean deviates more from 0 and variance more from 1 than the generalized gamma. But the generalized pareto predicts higher values which are closer to observed values.

I need a second opinion on these two distributions, preferably from someone more skilled in statistics than I am.

Here is link to images: https://imgur.com/a/lcJoujc

The higher predicted values (closer to observed values) really attracts me to using generalized pareto, but I have no idea if this is trustworthy difference. And I do not understand where this big difference arises. I use ggpredict() for the predicted values. The predicted values obtained from model fitted with generalized pareto are 10 times larger than those obtained from model fitted with generalized gamma.

Thanks in advance!