I too live in Oxford (been here for about a year) and unless I have totally and utterly missed the decent stuff, Boars Hill is completely and utterly gash for riding. I have only ventured up there twice, mind; first time in the wet and found nothing apart from mud; second time in the dry and found nothing but baked hard horse hoof prints.
Shotover seems okay although it depends on what sort of thing you want to ride, really. There are some of the gayest dirt jumps (and I use the term 'dirt jumps' loosely there) over towards the east of it, and a couple of okay but very short DH runs further across towards the car park – at least that's what I've found so far.
The only place I've ridden in the Chilterns is Aston Hill a few years ago and as mentioned, it's a slippy, greasy hellhole in the wet, and doesn't deserve it's self-given monicker of "best DH location in the SE". Don't get me wrong, it's a decent place for a dick about and some of the DH races used to be a good laugh but don't expect to find a chalky Innerleithen.
I tend to drive to the Surrey Hills a fair bit, mainly because I know the trails and I know people who ride there. I think the slippyness of chalk has put me off trying out the Chilterns, as well as lack of knowledge.
With all the above taken into consideration, I would be happy to be shown better stuff around Oxford so may also email and join you for a night ride, if that's cool? If I am slow up hills, you'll just have to wait.