My brother also has an APS3000 machine in San Clemente. I've got an evaluation version of Shape3D on my PC as well as APS3000. The programs from a design standpoint are very similar. Shape3D has a Master Scale that is pretty easy to enter the critical dimensions and both use control point tangencies like Adobe Illustrator or AutoCad to manipulate curves. At this point the major difference I see between the two programs is how they make the data available. But, then I've never cut from a Shape 3D file. APS3000 makes their software available for free but will not accept other software data or output universal translator files like iges. Shape3D will accept and export iges files or DXF files, but the software costs to use aside from their valuation version.
I’ve cut on APS3000 and a KKL using Shape3d software. The results are similar - more the attention of the operator in setting up the blank and (I think) defining the cutting path and the quality of the blank. You can pay more and get a finer cut on both machines and probably not be able to tell the difference.
Shape3D is software not a machine. APS3000 is software as well as hardware but APS3000 software is only intended to run an APS3000. Shape3D runs just about anything as far as I’m aware.