"Would just as soon" seems to get used two ways. It can either express a preference or simply a lack of one.
For example, if someone is asked if they'd like to go for a walk, with the reply "I would just as soon stay in", they're actually saying that they'd prefer to stay in.
However if I was to say that "I would just as soon go to McDonalds as to La Gavroche", I'm not actually saying that I want to go to McDonalds, or even that I'd actually enjoy going there; I'm simply expressing a total lack of interest in dining in posh restaurants like La Gavroche.