Actually, there is a distinction without a difference. In either model, when the customers go away so does the money. When that happens, the owner better figure out a way to attract more customers, or reduce the expenses. Business 101.
Dittos
Freepathons have been running longer and longer, well before the current kerfuffle over zotting Romneybots. Per that evidence, I don't see that one has anything to do with the other.
Sure, some donors are going to drop off because they've been shown the door, but there are new Freepers being made every day, and some of them will surely replace those donors who've left.
The truth is, the straight donation model has been somewhat of a struggling funding method for a couple of years now. The economy has simply tightened, and that's a fact.
I don't think there's any shortage of Freepers - just paying Freepers. A three tiered membership model, coupled with banner ads, is a proven way to bring in sufficient revenues to a site such as this. That's my suggestion.