Take it from an Oxford student and someone who's been very involved with the interview process. Oxbridge candidates are judged on two criteria and two criteria alone. The tutors let you in if:
1. You are intelligent.
2. They think they would enjoy teaching you.
Point no. 1 is the most important. The intelligence required is not the intelligence of the "i got 10 a stars and 5 a's at a-level" kind; it is a raw, base intelligence rather than a booksmart, swotty, revise-a-lot cleverness. They want people with a spark in them, innate brilliance.
Point number two is less important, but still incredibly useful. At the end of the day the same tutors will be in close personal supervision of you for at least a year; they want to be able to enjoy your company.
The only reason that point 2 is outweighed by point 1 is the "arsehole factor". That is someone who more than fulfils the criterion for intelligence set above, but carries with it an inflated ego and an arrogant, stuck up personality. Having had numerous conversations with tutors regarding candidates, the scenario they most fear is when the said arsehole is being considered. 90% of the time they feel that the superb intellect of the above mentioned a-hole is enough to merit a place.
It is also worth bearing in mind that the tutors already have about 75% of their intake selected before the interviews actually take place, and use them as a kind of "tidying-up" exercise to quality-check.
To hammer home the point, in my interviews, I told one tutor not to sleep that night as I was planning to shoot him as he lay, and turned up to another interview drunk, after less than 3 hours sleep. In my entrance exam i wrote about s&m fetishists.