I'd go prepaid card, not debit since it is linked to a bank account
Prepaid, if it is lost, you are only out of that much money unlike a credit card (can they even get one at that age?), you may be able to recover the money by calling them and say it is stolen/lost
Cash is just so much easier to lose track of, in my opinion. But I never liked cash to begin with. With a card, you can get those lanyards and hole punch the card and "wear" the card on the child (like they do to adults at casinos)
Draw back of prepaid card is getting that pesky unspent few cents/dollars off it. Though AMEX has a prepaid card that is nice, no fees, easy to get money back off it too.
I thought you could set "limits" on where a prepaid card is spent by limiting what type of vendors it allows. Like only "food" and "retail" places.
UK link about this and relates to this thread
http://www.theguardian.com/money/2012/nov/15/debit-card-childrenedit sorry didn't see you aren't in US? Not sure if you have the amex option
also as part of update, when you say debit, do you mean prepaid card? Not sure where but I've seen foreign references that imply something like this and not the debit card that we use in the US where it is linked to a bank account