I personally prefer the outlined versions as I think it unifies both sets of pieces. In the selout version, I see the white knights as having subtly more pronounced brows than the black ones, for example. I also think outlines would probably be more versatile should you change anything about the colouring of the board, although I'm new so do take this with a pinch of salt. Speaking of the knights, I really love them. They're simple, clean, and have personality.
All of the pieces read really well but the rooks seem to have become octagonal rather than round. I've done a quick edit where I've removed a couple of pixels of outline at the base of each section to round them out a bit.
I also noticed that your light source seems to be above the pieces and vaguely in the direction of the viewer (based on the knights) so I've added shading to the stem (

- not familiar with terms for the parts of chess pieces) to give it a more three-dimensional appearance. In the same vein, I've added highlights to the crenelations at the back since they would also be receiving as much light as the ones at the front (as in your selout version).
Finally, the outlined rook seemed to have a very harsh delineation between 'front' and 'back' because of the outline that appears on the crenelations at the sides. I've softened the shading there as well to hopefully also make it appear rounder.

I hope this helps!