as others have said
nannies are employed by yourself, you pay their tax and ni (on their behalf) and they are in your own home, and can look after as many children as they like (unless reg, then think mm will only insure up to 7)
cm are se, they look after children in their home, they can only have 3 under 5's
im a nanny, and think that different types of childcare suit different famillies, but 2 main plus's for nannies are that
nanny will come to house,andsort out everything,if you have a cm, you have to get yourself and children up,dressed and ready and then drop off
nannies will have ill children,many cm's dont as have other children to consider, so that is something to consider if your child is ill, can you time time off/find other childcare arrangements
nannies are gen more exp, but once you have 2 or more children , makes the cost worthwhile and prob if 3 cheaper to have a nanny then a cm