Depends on the regular shroom, but IME the regular shrooms will overgrow just about anything except some LPS (although they will overgrow certain LPS's like Lobo's.
I have always thought we needed to set up a Pokeman type guide with our corals... Shrooms beat ricordia and Zoa's, frogspawns beat shrooms, Bubble coral beats frogspawn, Acans beat Bubbles... and so on.