-ing is present tense “I am walking.” (Right now, at the current moment). -ed is past tense “I walked to the store.” (Previously, in the past). So in your example often-downloaded would be past tense, as in, “10 years ago, I often downloaded music illegally.” While often-downloading is present tense. “I am often downloading new updates for my program, because it has a lot of bugs.” This is something that is currently happening.

The dashes are not needed. "Downloading" has the ability to behave as a gerund. "Downloaded" does not have that capacity. For example, you can say "Often downloading is stretching the capacity of his computer" but that makes no sense if you replace "downloading" with "downloaded". When the phrase "often downloaded" is used, it is more likely that "often" will modify a verb than "downloaded": "That software is often downloaded" ("often" modifies "is").