Formigalouco
Hi all! Which MBA program is stronger and more reputable: Oxford, Cambridge or HEC Paris? I have offers from all three, with Cambridge and HEC Paris providing scholarships and costing roughly the same, both over $20,000 cheaper than Oxford. My post-graduation goal is to work in consulting or big tech. Any recommendations or insights you can share would be greatly appreciated

Congrats on the offers. It really depends on what you are after. Both Oxford and Cambridge have very similar reputations in UK and globally. HEC also has a strong reputation, but more so in FR and EU. If you plan to work in the UK after the completion of your programme, Oxbridge would be better suited. If you plan to work in France, HEC would have the edge. Outside the EU, Oxbridge would have an edge in terms of reputation/recognisability over HEC.
HEC has been ranking very highly on most rankings lately. Cambridge also had a recent jump to 7th on QS (just behind HEC at 6th). Rankings also change each year and it depends on the table (FT, QS etc.), however, all three schools typically rank in the global top 30, so I wouldn't let rankings hold too much weight unless you plan to apply somewhere where that matters (e.g. IB, MBB).
All three schools have similar GMAT entry requirements, average age of the cohort and % of international students. Oxford has the largest cohort at ~350, followed by HEC with 265, and Cambridge with ~250. All three have a similar portion of students going into consulting post-MBA, but not as strong for consulting as INSEAD/LBS (who MBB typically recruit from). Not sure about HEC for tech, but Cambridge might have the slight edge over Oxford for tech, whereas Oxford might have the slight edge for Finance.
In terms of Oxford VS. Cambridge, there are many posts comparing the two, but for me, Cambridge slightly edged it out due to 1) Smaller more intimate cohort, 2) More tech-focused (including being in Silicon-Fen), and 3) Smaller town than Oxford which gives it a quaint English "fairy tale" town feel (which was the experience I was after, coming from outside the UK). Oxford is still beautiful, but much bigger and more of a small city - Oxford is often described as a large town with a university in it, whereas Cambridge is a university with a town built around it.
In summary, they are all strong schools. If you have scholarships from Cambridge/HEC, I would lean towards these, then make your decision based on which city you would rather experience your MBA in, the curriculum that interests you more, and the location you want to work in post-MBA. Hope that helps.