Brandon James Greer did a sprite analysis of these portraits on YouTube.
He did not try to re-create them, but he noticed some useful things. Even though they are based on drawings, they're not simply resized. They're hand-made. And their palettes are less saturated to make it easier to re-use the same colors in different parts of the picture for things like anti-aliasing.
Gee... I wonder why.
Let's soften it up. And I'll restore my original ambiguous expression. This could be a smile or concentration. We'll let my words decide.
... aaaand done.
In retrospect, maybe I should have zoomed-in more. I think part of the reason why the Chrono Trigger portraits look better is because the original drawings have everybody is in these dynamic action poses. Apparently Akira Toryama is good at action poses... what a shocker.