If a BTEC is rejected (be that Cambridge, or whatever) then it is highly likely that particular degree course content is unsuitable to the type of learner that would choose a BTEC level 3.
Conversely, 3 A* in Maths, Chemistry and Further Maths won't get you onto a high quality, competitive degree in Art and Design. (If you happen to have those qualification - it will still be the BTEC/Foundation degree portfolio that gets you in).
Luckily, those designing degree courses have a far less blinkered view of the world and realise we need a cross section of skills in the real world from students with a cross section of academic versus vocational ability. I trust the Universities to write their application requirements to suit their course, so the students thrive and choose the right route.
That is why A levels are not better than BTEC. They are different and it doesn't particularly help when people try and assess one as better than the other. The answer to what is better depends on the student, their academic versus vocational bent and their intended career.
Some careers sit somewhere in the middle and I would venture to say mine, accountancy, is one of those. It needs a certain level of academic ability but equally, in reality, its a very vocational job and all the professional examinations require not just the exam passes but practical experience too. Their final examination is a case study, which puts theory into practice. I went the BTEC route, as did another course mate. Many of my friends in the industry chose to go the A level route. You can even go AAT route and with that you can miss out on BTEC L3 or A levels completely (or not).
Sorry I have gone on a bit but I do get very annoyed at those that simply give a concrete "A levels are best" answer. It depends on so much more.
My biggest concern for the OP would not be A levels versus BTEC but the lack of motivation and not being happy where he is because both are important to achieve potential.