Hi Conrad,
Oxford R2 applicant here....got dinged by Cambridge earlier.
Perception wise I'm not sure there are too many material differences between the two. Both have strong distinguished history of educating world leaders and stellar reputation all around the world.
I think (I might be wrong) JBS is perceived as a very selective program. We have tons of people who got dinged by JBS (without any interviews) who would have ordinarily thought they had an excellent shot at getting in. There appears to be some hidden quality the guys at JBS look out for in applicants. The Oxford admissions process appears to be more straightforward and predictable.
There's also the perception that the ethos of team work among course mates is more common at JBS than at SBS . Finally, I think SBS leans a little towards finance while JBS is more technology and entrepreneurship oriented.
Once again, I might be wrong....Just my two cents
To my fellow round 2ers.....just a couple more hours!