For bacterial spoilage, keeping the soup hot would be more effective. As for "preserving" the soup, refrigeration will be drastically more effective.
The high temperatures of simmering would keep the bacterial level pretty much nil, but the constant heat will ruin your soup on it's own. Anything in the soup will become mush, flavors will become over-concentrated, and some flavors can drastically change from prolonged exposure to such heat.
Prompt chilling and cold storage after cooking will greatly slow down the rate at which bacteria can repopulate the soup, and will also keep everything else in the soup about the way it was when the soup was at it's prime. To really keep textures nice, I'd recommend pulling off the soup that will be stored while vegetables & meat are still a little firmer than you'd like so that they'll finish when you reheat.