I was an acoustical consultant for ten years. This is one of my spaces.
Egg crate is useful solely for reflected sound. It's an absorber. In order to have any noticeable effect, absorption must be substantial portions of your room. As in, floor (carpet), ceiling (acoustic tile), two walls (drapes). It has negligible effect on noise penetration across the partition because penetration noise is governed by mass law. Foam has no mass; it's useless for penetration.
You don't mention what you're trying to accomplish. If you're trying to keep noisy stuff from crossing the door, your best bet is to weatherstrip around the perimeter. Assuming it's a foam core door, your next best bet is to replace the door with one that's heavier (and weatherstrip again). If you're trying to kill echo in your room, you will benefit far more from putting down an area rug.
Sorry to be a buzzkill. egg crate is really ineffective at anything other than preventing damage in shipment, which is what it's designed for. Acoustics is tricky and expensive and that foam pad will do you much more good under your sheets than it will on your door.