Which is a better option?

[Munchkins122]

A nanny being paid as per the hours she works (One quieter week, the next week a little busier) or a set amount paid each week?

Depends on the nanny. The person doing the Payroll will probably prefer it to be the same amount every week, all year round.

Nannys argument is that she could have 3 lower paid weeks and 1 week at a slightly higher rate. This will send her monthly total lower than if she had consistent set pay every week of the month.

I don't understand. Perhaps give some figures?
Either you are doing weekly payroll or monthly payroll, you can't do both. So are you both looking at the monthly total, or the weekly totals? 4 weeks does not equal 1 month, so you would need to do calculate for 52 weeks and then divide by 12 to get monthly.

Why would the hours vary so much

Does she have set hours each week that she is expected to work or does it vary each week? It sounds like she wants a guaranteed number of hours per week that she is getting paid for yet you aren't giving her set hours and only want to pay the hours she works?

Do you want her to be available when you need her if so pay the same each week so she knows where she is and can live if you are happy for her to say I've booked other work that week stay adhoc.

Average it out over the month and pay a set amount.

For example I pay my childminder the same amount per week, she provides wrap around care for school. This set price includes all day cover during the school holidays meaning I don't pay extra to cover and she knows what's she's earning