I don't think it's a particularly important factor, personally, as you can't help what board the institution you're studying at does. The boards clearly have general reputations but, as ever, every thing changes from year to year, level of study and module to module and I've known people that have marked for two (or more) exam boards who haven't claimed that particular trends exist. Futhermore, the Oxbridge admissions has loads of factors that it considers, so I shouldn't imagine that it's a major one.