I got the large structured men's Sac de Jour and I live in Toronto so I don't have the same problem with pickpockets, but I can't imagine it being very easy to steal from even though the top is open. I have a hard time getting into the bag myself. I don't want to undo the snap closures but it makes it very difficult to get anything from my bag. I can drop a wallet in but it's difficult to fish out without having to drag the handles open, which minimally makes the opening wider.
You can always store valuables in the zippered pouch inside. That pouch cannot be stolen easily as it is snapped in, and the zipper provides extra protection against thieves.
I also have the Sac de Jour men's 48hr duffle and that bag has a zipper all the way across the top. It may be better against thieves, as mentioned by
@coolmelondew . It comes in a few sizes including a rather small one that works perfectly as a purse. It depends on if you prefer the structured version over the supple version, since the duffle only comes in the supple version. I am not a big fan of the supple version of the original Sac de Jour, but I love the supple duffle because I find the unstructured leather works beautifully for that design (it is meant to be a duffle bag after all).