I thought the wainscotting was behind the wood trim, I didn't see that you inlaid the panels. Tight work!
I actually do like how it looks now, with the white panels surrounded by the wood, something which I normally don't like... in this case it doesn't look too bad! Honestly I think all one color would be the best... But if you ask 50 people, 25 will say they like one way and 25 will like the other! Either way you did a great job and it looks like something you should be proud of, so don't sweat it too much.
The thing about the dark wood against the white is what bothers me... If you aren't going to paint it all one color, I would leave the wood clear or blond like it is now. It would be too much of a contrast against the white of the bead board. Instead of a stain, you could do it a dark painted trim with a slightly lighter shade of the color you painted with for the inlaid panels... This would keep it all in the same family of color, but still give you a contrast.