Per hour, part time nannies might make more than share nannies. Might being the key word. Shares start out at $9-10 per hour per family.
Part time could mean anything between 10-30 hours. Some might say anything under 40 is part time. From what I've seen, most full time nanny jobs need at least 45 hours.
A part time nanny working only 20 hours might make more per hour than a nanny working 30 hours part time.
I don't understand why there's an argument. As with every nanny job, rates depend on location, number of children, hours worked, and benefits.