Most Breps are converted to meshes directly on the servers, using the Rhino meshing algorithm. That’s because the online viewer needs meshes for display. During this operation, the texture coordinates of the Breps are applied to the meshes, and therefore should be identical. Can you give more precisions about the setup of your definition?
As a general comment, I would strongly recommend that you convert your Breps to Meshes manually in Grasshopper before uploading your definitions. There are several reasons related to performance and reliability. You can read more about it here.
It’s true that the file size of your definition might get bigger when using meshes, but this won’t affect the performance on ShapeDiver, and overall shouldn’t be an issue unless your files are bigger than the allowed limit (40mb for free accounts). Also make sure to save as binary .gh and not .ghx.