The soft proof and output should match (reasonably close). If not, there's an issue with the profiles (display or if unique to this one paper profile, the two possible tables in the paper profile). If you toggle intents and see something you like, you should get this on output. That one intent in one profile may be preferable tells us something about how the profiles and their rendering is produced. IF you had two paper profiles, both produced output and matching soft proof AND you prefer how one handles the rendering over the other, use the one you prefer. Again, with perceptual rendering, each profile maker will produce a different result. Just like when you set a bunch of cameras to shoot a JPEG, each will produce different color from the same scene. Its not colorimetrically correct. With the Colorimetric tables, yes, they should match (but often don't).