LAMDA is the more recognised & established course - it's probably the oldest drama school (conservatoire) in the country. Oxford DS is well-respected, but doesn't have the immediate notice that LAMDA has, nor such good connections to the profession.
But - the thing you need to think about, however, is that if he's not ready/good enough to get into the main degree programme at LAMDA or RADA or East15 etc etc (these are courses eligible for student loans, and offer degrees) then is he good enough right now to spend money on a "foundation" year?
There are many many drama schools which will take your money but the offer of a place is not an indication of the requisite qualities to make it in the profession.
Sometimes, young people need a bit of life lived before they are in the right place for drama school. I come from a family of professional performers (dancers & actors) and the dancers need early intense training, but the actors didn't really hit their strides till mid-20s. They did all sorts of other stuff before going into full-time drama school - which they kept doing while auditioning and in between show contracts.
95% of actors are unemployed. And I think most people outside the profession underestimate just how talented (AND lucky) you have to be - just how talented, mostly, to make it in the profession. What looks like a talented young person in a school play or youth drama group may not quite cut it in the actual profession.