Choosing algorithm depending on tree data structure

I have a data tree which is very wide. I have under 1000 nodes/file and never more than 4 levels deep (counting the root element as level 0).

Now I want to calculate the difference between two of these trees. so far I have been looking at different algorithms for tree edit distance (Sasha/Zhang, Demaine and Pawlik/Augsten).

I wonder if there are better suited algorithms for tree matchings with this structure? I do know where most of the changes will occur within the file, and I figure I should be able to use this in order to speed up the process if I need to multithread this operation, maybe I dont need too since I dont have that large files?