Yes, the sheet has far more give than the wall, thereby significantly slowing down the impact.
The sheet that is hung and stretched tightly still has more than enough give to slow the impact down enough so the egg won't break. We did it in college physics lab. And one of the throwers was an NCAA all-American pitcher. And he couldn't break it.
Being a middle school science teacher, I also do this with my students. The only eggs that broke on the sheet so far have been eggs that were cracked already.
If you pull the sheet tight enough by using some sort of tensioning device, you might be able to break the egg. Then again, if it's that tight, the sheet will probably tear first.
Did I go too far with the information... probably.