I would think anywhere you'd be likely to be pulling a cart to, you'd be better able to get there (carrying even more stuff) using a 4x4 truck. Your truck would eventually run out of gas, but not before you'd already made it further than you could drag a cart in a month or two of walking. The exception might those situations where your see refugees trying to evacuate their country for the borders of another, across a relatively flat desert or similar terrain.

I'd say for the typical urban dweller, a backpack for no-advance-notice evacs, and a 4x4 truck for when you have more time would beat a hand-pulled cart any day. If you really want to be prepared, have a fully stocked trailer ready to be pulled by your truck. Possibly even stored away from your home, along your planned evac route somewhere.