Replacing old stucco with new

Our house was built in 1966 and is a single detached two-story. The top floor is clad with old stucco with a pebble dash finish. It is in decent shape but with some small minor cracking on one of the sides. We want to replace it with the new acrylic stucco to modernize the house.

Should we have the old stucco removed before applying the new acrylic stucco?

We had two stucco companies around for estimates.

The first company initially said that it wasn't necessary to remove the old stucco but when we prodded further, he said that they could take the stucco off on two of the walls because the other two seemed in fine shape.

The second company said that they don't see the need to remove the old stucco.

Both companies said they will put a layer of styrofoam on top and a mesh with the base coat and then a final coat of stucco.

Both companies said that keeping the old stucco will improve the insulation, and given the age of the house, once you start taking things off you're not sure what's underneath.

What is the proper procedure?

We're confused because we thought the proper way was to have the old stucco removed but we're also concerned about finding a can of worms underneath the old stucco if we do have it removed.