As I understand it
_AlignVertices sets the vertices in question to the same position or location.
_Stitch does the same, but is less specific about the geometry type it expects. Not only does it work with vertices, but with control points, and edges too.
! _Stitch can do anything ! _AlignVertices can do. Can I understand it this way?
AlignVertices works from a tolerance and works on vertices ,
Stitch does not care about how far way the inputs are, and takes edges as inputs , also Stitch lets you place the new location.
I would tend to think of
AlignVertices more as a repair tool,
Stitch as an editing tool.