My DD finished IB this summer. In comparison to A levels:
Maths:
HL is like further maths, SL is basically maths A level without the mechanics. Unlike maths A level (at least the board I'm aware of) you have to do a project, which I think is brilliant - using your maths knowledge in a way that's meaningful to you. My DD, as a potential medic, did hers on formulae to predict the spread of disease. I'd have loved having the chance to do this back in the dark ages when I did A level and found it completely unrelated to real life.
If you take SL, and have a uni offer with HL specific grades to make, it is tough to find the time to do your maths justice. Many, many people underperform in maths SL. Having said that, the maths has changed now. There used to be an easier Maths studies option, but now it's maths analysis and maths applications or something - not really sure if the applications is a properly manageable option like the old maths studies was. But if your DC goes for IB, don't underestimate the challenge of doing the more difficult maths options.
English
I LOVE the IB approach compared to A level. You do a lot of texts, a pair at a time, get assessed on them in some way (mix of presentation, spoken analysis, essay) and then move on - at least for SL you do, not sure about HL. The final exam is only on the last group of texts, when you've got a lot of your marks in the bag already. My DD did a Greek tragedy, a Shakespeare play, a Victorian novel, part of Paradise Lost, a modern play, a modern novel, Donne, Plath and Auden poems (and probably some other things I've forgotten). Really stimulating course. But maybe A level would be better if you hated giving presentations.
MFL
No translation, unlike A level. A lot of emphasis on good ideas in debates and essays as well as good use of language. It's testing your intelligence as a thinker/writer, not just your fluency in the language. (This may be the same in A level - not sure - but there definitely seems to be an encouraged multicultural IB way of thinking). If you don't fancy AS/A level MFL, you can do an ab initio course that gets you from beginner to around GCSE level.
Biology and Chemistry
My DD did HL for these. Think it was pretty much the same syllabus as A level, so a lot of work with all the other subjects on top. She's now studying medicine and hasn't felt behind at all on the science front.
Again, unlike A level, there's a project/investigation aspect to it (20% of total marks, maybe?). This was not as personalisable as in maths, at least at my DD's college, and was pretty high stress. Good preparation for a science degree though, probably.
History
Both HL and SL involve an extended essay. Not sure if that's true for A level.
Each subject has an extended essay or project, and then you have to do a separate extended essay on any one of your subjects. So a lot of coursework going on at the same time, which needs to be kept on top of.
Uni offers are more complicated than for A level. Most give a minimum for overall points required (out of 45) plus requirements for your 3 HLs. Some also give specific requirements for your SLs. There's quite a lot of variety with unis in translating A level standard offers to IB, ie. AAA might be 666, 665 or 667. BUT there's often more leeway with missed grades for SLs/TOK/extended essay on results day (or in my DD's case, A level results day, which is 5 weeks later - she was in limbo for those weeks but it all came good).
In summary, it's a lot of work, high stress at times, extremely stimulating, great preparation for uni. Not the easy route by any means, but my DD has no regrets at all.
Sorry, that was a bit of an extended essay in itself!