ABOVE is the original photo to be converted to vector outlines. The client also asked that I drop the background, separate the two cats, and complete the areas (feet and tail) that were cut off.
I dropped the bkgrnd, then, as an experiement, ran the highest quality Auto-Trace. The result, above, looks very similar to the low-quality orignal, with banded gradients, even including some of the pink color. (Given a better original, this method might work better.)
The vector outlines created by the Auto-Trace were extremely rough and complex and so did not produce smooth gradients. This amount of complexity can slow down and cause complications in the output of the final file. (Your pre-press guys will hate you for this!)
The outlines creatied by using gradient meshes are much more clean, providing a smooth, even blend in the gradients. They are also much less complex, and so will not cause problems with the output.
My final artowrk, using shapes drawn with the pen tool and converted to gradient meshes. This method gave me much more control over the final art, including being able to create a limited palette of 11 colors, rather than letting Auto-Trace determine the colors.
So, as you can see, my final art has much smoother gradients and less complex vector outlines, for a bettter result in both how the file looks and in how it will work.