The unshakable truth is that you are using two different papers. Very possibly, one of them doesn't have a good profile. Plus, it sounds like they have quite different surfaces.
What printer are you using? Also, are you using the printer's driver or a RIP? Have you turned off color management in the printer driver? (Let Photoshop manage the colors.)
Have you soft-proofed using both profiles. If so, how do the soft proofs compare? How does each compare to no soft-proofing?
Why not proof with the same paper on which you plan to print your enlargements? Give this a try and compare the 4x6 with a 16x20, or a portion of the 16x20, and see how these two compare. Of course, you'd be using the same profile for both.
If you still see a big difference, then perhaps you're seeing compressed details in the proof as Lenny suggests. But until you try using the exact same paper, profile, and printer resolution for the proof and final enlargement, I think it's premature to draw that conclusion.
Interesting; I've not heard of compressed detail that Lenny describes. I tend to print small. I'll watch for this when doing significant enlargements in the future.
I would think that the difference is due to the paper. You should be able to see that difference also in soft proof.
As Neil suggested, print a crop of the 16x20 in a 4x6 Epson Glossy and compare.
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