Do all jobs come from Integrated at OATS
By "all" I think you mean "most". I am somewhat uninformed as not having a direct line into the JAA statistics machine. However I would hazzard a guess that BAE or Oxford share the majority of successes when compared to any other single organisations. Which of BAE or Oxford give you the best chance? No idea! Also, the quality can not be guessed at unless the successes can be measured against the numbers of students and I assume there is no reliable independant data to extract this kind of useful information.
Furthermore, even if you knew this, it would not help as that does not mean that you have increased your personal chance of success.
All the top schools have a good reputation. I suspect your chance of success will be 98% persperation and 2% location.
Good luck!