For me it does depend on the individual and what they can do for my child however we are in the process of choosing Housemasters for senior school and we tend to go for the ones that have interesing lives outside the classroom. We also choose Housemasters who have strengths that DS does not have e.g. an English teacher instead of Maths or a very sporty teacher as we feel it may help to broaden his outlook on life.
As for specific qualifications, I am all for a teacher having experience with many age groups although I may worry that someone used to teaching adults may not be able to come down to a young child's level but I have no evidence that this is the case.
From an independent sector view point I often find that a teacher coming from the state sector is less flexible and initially very strict in their first couple of years because they feel they have to prove themself in the private sector when in fact they are probably already better teachers than many already in the independent sector.
If I had to choose between a teacher with a degree in the subject that they teach - and a passion for it - and one without but a teaching degree, I would probably choose the former although ideally a teacher would have both.
I'm not sure if this was the info you were looking for or if I am WAY of topic!