I am using pink/blue/green styrofoam board on my layout, but took an extra step I learned here on the forum several years ago to help with quieting the sound of the trains rumbling down the track.
After building my benchwork and before laying the 5/8" plywood and the styrofoam onto it, I went to Lowe's and got a roll of hardwood flooring underlayment and cut it into strips and glued them onto the framing. Then I attached the plywood to the frame with only enough drywall screws to keep the plywood flat, then attached the styrofoam with 'Liquid Nails for Projects'.
Along with the Woodland Scenics foam roadbed and the room's carpeting the only thing you hear when the trains are running is the occasional clickety-clack and the locomotive electronic sounds. The roadbed and the track are attached with two-sided carpet tape, with one screw at the apex of the wide radius curves.
The styrofoam does get some dents and scratches, but I can incorporate that into the scenery since I'll be carving into it anyway. When painted it hides a lot of the imperfections, especially when ground cover is added.
I used a 2"X3" board as a straight edge to cut the material to match the width of the framing:
Here you can see the layers:
