Considering that we render in Tris, and if you provide a Quad mesh then your mesh is going to get triangulated by the renderer. Different rendering applications might triangulate your mesh differently which can produce inconsistent results.
My work flow is like this:
1. Keep a quad version that you can work on as quads are easier to deal with.
2. Before baking, and texturing your mesh you will want to convert your quads to tris and make sure you're alright with the shadding.
3. You can now continue to use your tri version of your mesh without worrying about any problems as the renderer doesn't need to convert it so you wont get different results per application.
This has always been my understanding, and if I'm wrong someone please correct me.