One table with a flag or two tables
Maybe you don't expect this answer, but do both. Let's see.


In order to accommodate for the life-cycle of the data ( something many database designers don't contemplate ), you should have a "historic" table with the downloads that finished. That table will not only hold files that downloaded successfully to a 100%, but also downloads that were canceled or aborted. You could have a policy of deleting records from this table after some given number of days.
The "live" downloads are in other table. Keep in mind that for the sake of simplicity, the migration of records from the "live" table to the "historic" one should be asynchronous (maybe a cron job or timer), meaning completed download will live there for a few seconds, or minutes after they finished. There's nothing wrong with it. It's even desirable so files don't disappear from view the very millisecond they finish downloading.
Add two timestamped columns to each table: TimeAdded and LastModified.
Why do I say this is both ? As I see it, it's a combination of the two approaches. Table one behaves as if you'd chosen the single table approach. Only an asynchronous process migrates completed or aborted files to a historic table after some time, it doesn't have to be immediate.