How to compare paired count data?
For visualizing paired 1D data, i.e. true vs predicted counts, you may use something like ggpaired.



You may also visualize the distribution of differences, where each sample is the difference between the true count and its predicted value; excluding the zero differences could better accentuate any deviation.

For a statistical test, you may use Wilcoxon signed rank test (python), or alternatively Sign test if the distribution of differences (true count - predicted count) is not symmetric around the mean.

It is worth noting that a statistical test may lead to "not the same" (rejection of "the same" null hypothesis) for an arbitrarily small difference when a large enough sample is provided, so be careful about the interpretation of "significant". For example, the statement "predicted counts under-estimate the true counts" could be statistically significant but with mean difference 0.05. Although this difference is statistically significant, however, depending on the task, it might be negligible. Therefore, for example, reporting the "mean ± std" of difference along side the statistical test would help interpreting the "significant" better. Also, take a look at this post on effect size.