Metrics to analyze branch lengths in phylogenetic trees
There are a variety of measures of tree similarity implemented in the TreeDist R package. (Your phylogenies appear to be from the R ape package, so hopefully you are somewhat familiar with R.)
Other tools include treedist from Joe Felsenstein, which computes Robinson-Foulds and the Branch Score Distance (which sounds closely related to your interests, described in this paper). You can see that software page for a lot more information.
For a practical description of the different tree comparison metrics you can see this article.
I would suggest taking a look at the manual and the multiple vignettes associated with the TreeDist package to learn more about how exactly those metrics work. There appear to be a wide variety of metrics in there that I have never heard of, such as clustering entropy or split entropy or Nye similarity.
This package also includes tools for making visualizations of differences, such as that shown below: