There are pros and cons. Freelancer may be cheaper but if there is any issue, you won’t be able to change or go to the agency. On the other hand, not all CLs from agencies are good and you will have to pay more for the good ones. Also, agencies charge a lot more than freelancer. In my opinion, if you can find a freelance nanny who is really good and charges a reasonable rate, you can go with that. If not, find a reputable agency and just pay the fees.
Get freelancer first. Fire her if she is arrogant or troublesome then get new one from agency. Before that make sure agency allow you to make urgent request. There is risk for this option.