I don't know about how easy they are to deal with at the top corporate-to-corporate level - you hear all sorts, to be honest, about all voucher "providers", which is the middle-man thing BusyBees do. [Other main player is Accor - I'll put further details of what they actually do in this process in a separate post in case of boringness.]
But my employer uses them, and my employer is notoriously not unsharp. So they can't be bad. They certainly have a big segment of the market, so (relatively) know what they're doing.
Next - user-friendliness as regards the individual nanny-employer (or nursery-user): this is basically fine, if a bit plodding - you need to ensure that your childcare provider is specifically registered with them (as opposed to Accor or Vouchaz2U or whatever); and then you have to work within the parameters of quite limited payment systems to make the payments you want.
So, for instance, I would love to be able to set up a standing order from my saved-up stash with BusyBees so's I could pay my nanny a standard amount for the next x weeks - but can I? No. I have to go into the system every Monday, manually authorise a payment to go out that week, & pray it gets to her by Friday. If it doesn't, then I pay her separately & the late payment has to go to cover the following week.
It seems to me it should be shamingly easy nowadays to set up systems that can handle repeating payments (calendars can do it with appointments, and I do think BusyBees can handle monthly regular payments), and the BusyBees system is not a shining example of modernity, flexibility & speed. However, they haven't made mistakes, and other than the clunkiness of system & uncertainty of receipt my nanny is entirely happy.