Very interesting Joy, I think you are spot on on the factors that are different, but I think that is primarily because the entire underlying way that SERP is returned is different. Basically it's not an issue of the factors themselves being different but the entire framework for how the SERP is returned is different.
Consider this, when you do a keyword (non-branded) search Google is looking to answer your query by providing results based on their understanding of relevance and prominence. When you do a branded search though, and Google recognizes it as a branded search, they are returning entity specific results (hence, how they know and return a branded SERP, they know you are looking for an entity).
Basically it's PageRank vs. HummingBird/RankBrain, if that makes any sense. I've been deep in massive amounts of ranking factor data for months so I may just be speaking in tongues at this point.
Though again, I'm unconvinced brands themselves should care about optimizing for branded searches. This is much more of an issue in franchise/proprietor models as those are the people who care. Most brands don't want to get into picking winners among locations or fanchisees.
