To determine the appropriate statistical test to use, consider the specifics of your models, the type of data you have, and the results you want to compare. Here are some options:

If your models produce continuous outputs and you want to know whether one model produces higher or lower outputs than the other, consider using a paired t-test (if differences are normally distributed) or Wilcoxon signed-rank test (if differences are generally not distributed).

For binary classification results (e.g. positive/negative, true/false), if you want to compare error rates between models, consider using McNemar's test, designed specifically for comparing two classifiers.

If your models produce more complex outputs (e.g. predictions of multiple classes), consider using a one-way or two-way ANOVA to determine if there's a significant difference in their outputs.

For categorical outputs, use a Chi-Square test to determine if there is a significant difference between expected and observed frequencies in one or more categories.

Finally, non-parametric methods like Bootstrap or Permutation tests can estimate the distribution of a statistic under the null hypothesis and compare two models based on any statistic computed from resamples of your data.

You could test for contrasts between the two tests