We're getting our small 1&1/2 story 1952 house resided with vinyl. How much of the old should be removed?

The first contractor says remove the old aluminum siding and the composition board to get to the older wood clapboard. Cover with foam backed vinyl (R=3.5).

The second contractor says remove everything down to the structural siding and cover with foam backed vinyl (R=4.0).

The first sounds like a bad decision; the second sounds like the exterior walls are weakened, no gain in insulation, and the windows stick out.

What's the ideal? What layers should be removed and what material should be added to bring the walls back to the original thickness and strength?