Hmm. Are there bones in your character? I just noticed you're using deform>import/export skin weight. If there are bones, you should be using skin>export/import weight maps for the bones. Outside of that, the following UV stuff still applies for deformer skin weights.
If your UVs don't match between the new and the old version of the model, you will get unexpected results, because the skin weight map is created from uv positions of verticies. Another issue that can occur, is if your UVs overlap. For example, if the right arm UVs are in the same spot as the left arm UVs, you'll get weird results because it can't figure out what arm gets what weight.
If UVs are the problem, you can try creating a new UV set for both models. In the new UV sets, apply an automatic unwrap for each. The automatic unwrap will make sure each vertex gets a unique UV position. If the automatic UV unwraps look identical for each model, you should be able to export and import weight maps correctly with that. Once you're done, just switch back to your original UV sets to see the textures correctly.
If your character only deforms from bones, another possible option (maybe easier) is using Copy Skin Weights. Copy Skin Weights doesn't care about UVs. You can import the old model into the new model scene, and copy the skin weights from the old mesh to the new mesh using skin>Copy Skin Weights. Even though the meshes are bound to different skeletons, Maya should be able to push the weights to the new mesh and its skeleton. The bones and bone names HAVE to be identical though.
I know that's a lot of information, so if you need more information on any of it please let me know!
And as always, test this out on a copy of your file first!
