The two biggest factors are starting quality of the bike and how much it has been neglected.

A bottom end bike will tend to be garbage after 25 years even if it wasn't neglected. A nicer bike will require severe neglect to reach the same level of un-rideability.

If you look at previous year's entries in this contest, I think the more memorable bikes are ones where there was a high pain level at some point. The bike was difficult to get, or frustrating to work on, or a struggle to get dialed in, or embarrassing/uncomfortable to ride.