Nursery duties are basically anything to do with the children that isn't childcare. For example;
Clothes - washing, drying, ironing, putting away, mending, buying, sewing name labels in, clearing out any that are too small.
School - going to any school events parents can't make, sorting out homework/projects, baking for the cake sale, making the costume for book day/nativity play etc.
Bedroom/Playroom - tidying, organising, light cleaning, changing bedding, sorting old toys etc.
Social - hosting playdates, responding to invitations, party planning, taxi driver
Health - take to doctors, hospital appointments, speech therapy, optician, dentist
Shopping - food, shoes, clothes, nappies, birthday presents (for them or for a party they've been invited to), household bits.
Extras - feed/walk the dog/cat/hamster, wait in for parcels/workmen, collect the dry cleaning, pay the window cleaner, batch cook (so you don't need to on the weekend) and more.
A nanny may not do ALL of the above, it will depend on hours/number of children etc., but that all falls in the category 'what a nanny will do that a childminder won't'.
I would always go for a childminder over a nursery. In terms of childcare, they're great, they just don't offer the extras that a nanny does.
(Once you get to two or more children a nanny is comparable or cheaper in terms of cost).