It really depends. I said function because the object has to work on some level or there's no reason for owning it. However, I would accept lower levels of functionality in some things for aesthetics. I guess I'd separate the to into groups of things that I "need" versus things that I want. Need isn't exactly the right word (I don't "need" a couch, but function is much more important for a couch than say, a picture frame). Things I want can have a range of functionality and aesthetics.
Things that I need would be objects I use for everyday functioning: furniture, appliances, car, etc.
Things that I want would include: video games, movies, books, decor, music etc.
For games, I'll happily overlook buggy mechanics (especially for indie developers) to experience an interesting/unique narrative, style, or environment. I will not tolerate a car that needs to frequent the mechanic regardless of how much it resembles sex.