That is a great question!  I use the Fleurville Rerun Messenger and I would not suggest that one for a long day out - especially if you need any formula that has to stay cold, unless you don't mind having a separate cooler bag.  It would work for juice/water cups (outer pocket on each side) for a regular outing where you might need a few changes, extra outfit,small-medium wetbag, and small snack.

JJCole has one I want to try that looks larger.  I am not sure how deep it is though.