Simple. IB is much harder than A-levels, because of the fact that not only do ib students go through the academically rigorous process, doing 3 HL and 3 SL subjects, but also they have to finish their CAS,EE, TOK, IAs as well, which are taken to actually 'grade' the students. Whereas A-level students, although in general we do 4 AS subjects and 3 A2 subjects, don't get as much tension as ib students do as we only get assessed on the examination and small amount of coursework without any bull**** like CAS and TOK.
To be fair, though, A-level subjects can be comparable to IB. For instance, if one takes Mathematics and Further Mathematics, he or she has to take at least 12 modules or more if further modules are taken. Also, for Sciences, students are tested more extensively as they have to take 6 exams + coursework for each one. And A-level students learn more in depth topics; in Physics we learn Relativity, Astronomy, Engineering Physics, Optics compulsorily when IB students get to choose to learn only one advanced topic among 4.
The fact that IB students have to study the subjects that they don't have a flair nor interest at is frustrating and it is not something I would want to experience. I know IB is unfairly underestimated and A-level is "overestimated" in UK, but 32 or 33 equivalent to 3As in A-level is more unfair judgement. Considering the fact that if an offer for A-level is 3As, then IB offer is likely to be 36 at least. For 3A*s, IB is 42 or higher. So they're not that different as one of the 'parties' would want to believe so.
I'm studying at Imperial, and considering the fact that although for this first term A-level students just breezed it through, IB students were catching up what we had done in A-levels and all my mates from Mathematics who did IB say that they are experiencing the knowledge gap between them and those who did A-levels. So it just really depends on you.