I've been wondering this question lately. Is there anything that makes them particularly good? I always believed it was passives and move sets. One of the reasons I thought Rainmaker being able to fill the Fury metre in basically one move last year was cool and unique. He was 5*. Also, why I had objections to the Prisoner losing his ability to be a continuous passive dis-abler (now I object to it, because they'll never fix not blocking everyone's passives in PVP), he was rare as hell and a 5*.
I'm pretty sure it's only 5* tunes that have fury's too. And they might be story important characters.
The main 5 Eddie's for founders were 5* probably because they were a part of the promotion and unique looking. Visions, Carriage Rider, Samurai, Vampire Hunter, and Cyborg.