I cannot comment on the content of the courses, but as to contact time and teaching quality, contact time would probably be similar at both universities. Lots of contact with tutors are amongst the USPs of Oxford and Cambridge. Learning by discussion is the aim. Teaching quality will vary because it's down to individuals. Not every great academic researcher is a good teacher. Some of the teaching is done by early-career academics working on doctorates or post-doctoral research. Chance plays a part in determining whether you are taught by people with whom you form a good tutorial relationship. When it works, it's great. One reason why Oxford and Cambridge interview candidates is that the academics try to choose students whom they think that they and their colleagues can work well with for three or four years. They look for people who are, to use their terminology, "teachable".
My understanding is that Natural Sciences at Cambridge is a degree which to some extent the student shapes by making choices as to the courses taken, but others here or in the Cambridge thread can give you info on that. My friends who did science degrees at Oxford tell me that they did a lot of lab work, and indeed worked very hard in general. I studied History so was either asleep in the library or talking nonsense in the pub.