From the courses I took in canning and freezing home grown fruits and veggies I learned that freezing will slow down enzyme activity, but it will not stop it comletely. That is why many vegetables have to be blanched,plunged into boiling water and heated, to kill the enzymes before they can be frozen for long periods of time. In untreated products the deterioration of the product continues until it is no longer fit to eat. Of course it take longer for the product to go bad in the freezer than it does the refrigerator,and leaving it at room temperature makes it go bad even faster. This is just the normal way the progess of ripening works to prepare the fruit to begin its reproductive process.
Since we are looking to get our foods as fresh and "live" as possible. It would seem that freezing juice would keep more of the enzymes working longer than keeping it refrigerated. Of course fresh is best, but not always possible or practical.