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Foam will usually result in a lighter part, so it should produce a better weight to strength ratio.
Before anyone proves me wrong, of course it all depends on the shape of the part you want to build, and the direction of the forces acting on it. If the thickness doesn't matter, a foam core can be made thicker for the same weight. Stiffness of the sandwich increases with the cube (third power) of the thickness of the sandwich.
There is a reason why e.g. most composite aircraft are built with foam cores or honeycombs (because that's where weight really matters).
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