If you were cutting a contour with a bandsaw or jigsaw, you could stack the two boards on top of each other and cut them both at once. Then the left top piece would match with the right bottom piece, and vice versa.
I have done this by making a template of the edge, use that to trace the cut line on the wood, use a bandsaw to make the cut and then a drum sander to sweeten up the fit and "joint" the edges to get a good glue up.
I would use the band saw to make a single template out of 1/4" mdf. Obviously a bandsaw won't give you a nice smooth surface, so finish the template with a drum sander. Then use some strong double sided tape to attach the template to the piece, and use a router with a flush trim bit to make the cut. Then flip the template over and attach it to the second piece. This will ensure that both pieces have the exact same contour.
Yes, I've tried that. The drum sander does help to get the contours close. If many curves (in different directions), it's still impossible to get a perfect joint fit. Any mistake in sanding leaves a gap and the only way to fix it, is to drum sand the entire profile all over again - probably making another 'over-sanding' mistake.
The gaps may be small and can be filled with wood filler, however, I rather not see 'any' trace of wood filler.
Think of the contour as part of a template you would use when doing inlays.
Using the homemade template, cut one piece of wood using a Router Inlay Kit (see attachment) with the small diameter guide.
To cut the contour on the other piece of wood - add the bushing to the inlay cutter (to achieve the larger diameter guide). Now, using the same template, cut with the router.
There are limitations with this method:
1. The contour template should have only 'easy' turns of changing directions.
2. The radius of the curves should be much larger than the larger diameter guide (above).
3. The router faceplate should be supported over the entire surface (so it will not rock/tip).
The results will be close but not perfect. A drum sander will still be required to fix some areas.
I'm beginning to think that the old method of:
1. Create your contour template and rough it out with a jigsaw and smooth with drum sander.
2. Trace a pencil line on both pieces.
3. Do the jigsaw work and drum sander work on the two pieces - being very careful with the drum sander.
4. When 'close enough', give in and use a wood filler with the same wood color as one of the pieces. If the gaps are slight, they may not be noticed.