If you go on refining the mesh, while ensuring the mesh is exactly the same at all locations, then the difference should go on minimizing. When discretizing the model have you ensured exact same mesh? Also, what is "the percent" difference between reactions? Is 0.01 percent error? or absolute error?

Also, do you know about rounding off errors?

https://mathworld.wolfram.com/RoundoffError.html

https://en.wikipedia.org/wiki/Double-precision_floating-point_format

The numerical error can still cause a difference in results even the mesh is exactly the same! One-third model will give you reactions and you can assume that the other two parts have the same reactions.

On a side note, there are many things in the world right now that MUST be equal, but still, here we are!