I saw a demo on tv of what happens to a child's nightgown that is made of cotton when a match is set to it. The nightgown is immediately engulfed in flames because air is reaching a single thin layer of fabric from both sides. It is so fast that a child would be badly burned and hair would be on fire before anyone would have time to react. That is why so many cotton flannels are labeled "not for use in children's sleepwear". It's a no-no for nightgowns and loose-fitting pjs.
All-cotton sleepwear is fine when it is tight-fitting to the skin. You can buy some non-flame retardent cotton sleepwear like this because it is safe.
Polyester is not without its problems. The demo showed that it does not go up in flames; however, it melts into a sticky ball that can cling to skin and create deep burns. It is preferred because, if touched by flame, a poly nightgown at least gives you some time to get the child to safety.
I personally think all-cotton batting for a child's crib quilt is pretty good. The thickness of the layers means the quilt will not combust. A flame would travel slowly because it would be fed air from only one side; the other layers would be basically preventing air from feeding the flame from the other side. This gives someone quite a bit of time to react to a fire.
I do not think polyester batting is as good for a crib quilt because of its ability to melt and cling to skin. However, it may not make a difference. With either type of quilt, one would assume someone would smell something burning or hear a child crying before the fire was out of control.