These two programs use very different methods. Midas MeshFree uses Implicit Boundary Method. Even though it's called MeshFree it actually generates mesh but not on the boundaries - traditional FEM is used to solve the problem on internal mesh while boundary values ae calculated using special Dirichlet function.
Altair SimSolid utilizes the method of External Approximations. Pretty much all steps are the same as in regular FEA (same governing equations, matrices and solvers) but the discretization step is different. Instead of using a mesh made of regular simple shaped elements it divides the model into arbitrarily shaped volumes. Special shape functions (they neither have to be polynomial nor conform to continuity requirements) are created during the solution process.
Both methods are interesting and may be a serious competitor for traditional FEA in the future but I think that SimSolid's algorithm is more revolutionary. However these programs are new and it will take a lot of time to make them good enough to compete with such powerful software as ANSYS or Abaqus that were developed for many years and still are being improved.
