The shopping cart thing. . . I tend to think most folding bikes are too big and dirty to sit happily in shopping trolleys, if that's what you mean. One of the main reasons I'm hoping to become properly bonded to my Brompton is that it can function as a shopping trolley itself. . . whereas taking Dahons into shops is trickier.
I doubt local supermarkets would be happy with me putting a bike in a shopping trolley unless it was bagged, and the whole bagging process is a PITA (the bag itself is bulky).

As for public transport, if it's likely to be really crowded then all folding bikes are bigger than one would desire, and even a Brompton can be awkward.
I reckon if a compact fold is what you're after go for a Brompton. If you can make do with a reasonably compact fold and would like better gearing go for a Curve.