Hi
I have the WOC and it fits credit cards, money, my iphone and car keys plus lipstick. I dont have a mini flap so cant comment on that but I think the WOC might be more versatile for you as it already has a compartment for money and credit cards so you wouldnt have to also fit a wallet in (which I am guessing you would with the mini flap?)
I think the WOC is a great little bag - can be used as a clutch (with chain tucked in), as a bag (with chain doubled for shoulder bag) and messenger style across the body when chain is used fully. I think this would be most versatile for a new mommy but thats just my humble opinion : )
Also, it can be used as a wallet and put inside a bigger bag.
Btw, I did some searches on the WOC on here before buying mine - I am sure someone posted what they could fit in their WOC - have you tried the search?