I tried to split two simple meshes below with each other using MeshSplit command, but many intersections are missed. Most of them are when edges of the cutting mesh are overlapping triangles of to-be-cut mesh. V6 finds different intersection locations than V7 as visible on the image below.
Second issue, or attempt, was to examine the situation left by MeshSplit using MeshIntersect command. Interestingly, V6 command is better than V7 as you can see below, even though the V6 misses the rightmost triangle intersecting.
Finally, joining the two meshes and performing MeshSelfIntersect did not help.
Btw how are you dealing with tolerances for overlapping cases? Also, are you using geometrical predicates for these commands? It seems that MeshSplit command would be more robust if it would perform MeshIntersect and then embed edges that were found. If you need any help on the implementation that would avoid current issues, let me know.