I would say the answer depends on the size of the narrower gaps and if a halfway matching copy-bit for the router could be found.
If my measurements from the picture and calculations are halfway right, then the narrower gaps would be about 8mm wide.
If a bearing guided bit that size could be found, then the router is surely the better and especially faster choice.
Even if there would be minor tips and details, where an almost fitting copy-bit for a router might just not get in totally - the smallest bits I'd know of have 3/8", a router still could be the faster solution to hog out the majority of the material - only using e.g. a scrollsaw for the last tiny bits and details.
After all, you want to create 6 copies of the "master", not just one.
Therefore, only if not an even closely matching bit could be found, I'd go for 100% scrollsaw.
In regards to the choice of material, starting from about 8-10mm or thicker, personally I would perhaps prefer soft pine over plywood. Pine gives a warmer feeling than ply - which might be very welcome for a headboard of a bed. And since you plan to set the copies into a frame, stability would not be that much of a problem.
When life gives you lemons - make lemonade.... (1915, Elbert Hubbard)