I personally would paint outside and inside the boxes the same color and leave the trim as only an architectural decoration and not as a delineation of painted spaces. Painting the inside of just one or all of the boxes, it could be really jarring.
Were you thinking an accent color close to the wall color or completely different?
You could paint it all in stages: Paint the wall the color you like. Then take a large piece of poster board, cut it to the size/shape of the box and paint one side the wall color and the other side the accent color. Hold the board up there and see what you think. It's more work, but easier to paint poster board than repaint a wall :)

What about painting the trim a complimentary accent color? A much lighter color than the wall? You could also use paint to "faux" the trim into looking wider- follow the trimline and paint a 1-2 inch "border" on the inside of the box.

http://betweennapsontheporch.net/dining-room-upgrade-add-picture-molding-beneath-chair-rail/

Just look at her pictures. I think that will answer your question.

I might paint the trim a slightly lighter color but not the boxes.

All the same:

Compared to:

I think the link below is the one that Patricia meant. The one above took me to an outside table.

Here is a link that might be useful: Adding Picture Molding to the Dining Room