It seems that the question is not really about which one you should use, but when you should use both. As has been pointed out, Rhino and Maya are good at different things, but I disagree that Maya is predominantly good at animation. I don’t think it’s questionable that Maya is better at animation than Rhino, but it has a number of other things it excels at as well.
I am not an extremely experienced Maya user, but I have used it in conjunction with Rhino on several projects. I haven’t used Maya scripting at all, so I can’t comment on how it compares to Grasshopper or Rhinoscript.
As a polygon modeler Maya has a much easier time making some complex curved forms. Any surface that cannot be easily broken into UV axes Rhino has to make with multiple surfaces which means more places to preserve continuity and therefore harder to edit. Maya on the other hand can create very complex forms with a fairly small number of vertices, so manipulating the form is very easy. Once the desired form is found, it can be smoothed to increase the polygon count and exported as an obj or fbx and brought into Rhino. The challenge is that once the mesh is smoothed it has many more vertices and is considerably harder to work with in both Maya and Rhino, so you’ll want to make sure you make a copy of it before it’s subdivided in case you need to manipulate it later. Rhino geometry can also be meshed and brought into Maya as an obj or fbx if you’re trying to coordinate between the two programs.
For the sort of “freeform” surfaces that Zaha Hadid is creating, Maya makes it much easier to manipulate those surfaces than Rhino does, but it’s much more difficult to be dimensionally precise. I tend to bring the dimensional elements into Maya from Rhino, and then I do my Maya modeling around the Rhino geometry to get accurate dimensions. I then export the Maya model and bring it into Rhino as a mesh, which I can either rebuild using multiple NURBS surfaces or just leave as a mesh.
The newer versions Maya do a slightly better job at converting between polygons and NURBS, but I generally find Maya’s NURBS functionality to be close to useless. For the most part I’d rather keep it a mesh or model my own surfaces by drawing contours and lofting or sweeping or some of Rhino’s other surface tools.
I also just finished a project where all of the modeling was done in Rhino, and then brought into Maya to render with Mentalray. Rhino5’s texture mapping has gotten way better, but Maya still has some advantages in rendering. I haven’t used 3DS, but I understand that Mentalray has slightly different options between the two.
Maya also has a pretty substantial physics engine. There are now a number of plug-ins for rhino that can do form-finding simulations, but Maya has the ability to simulate draped cloths and particle simulations that are pretty advanced, and potentially a little bit easier than setting up a Kangaroo Grasshopper definition, but that really depends on where your comfortable.
I would also agree that Rhino is way more intuitive for a designer than Maya. Maya is one of the least intuitive programs I’ve used. I mean, why is E rotate and R scale?
Sorry for the long post, but that’s what I’ve found in working between the two programs. It’s definitely not a seamless transition, but I think that both programs have strengths. You just have to know what you’re trying to accomplish and which program is right for the job.