Guys, there are some massive generalisations going on here. While it would be nice to deterministically write down
Harvard > Oxford > Princeton ...
It simply isn't possible. Even ranking cars, or computers is tough - how can you objectively rank institutions that consist of thousands of students, academics, conduct teaching in different areas, have disparate amounts of funding, huge differences in fees, etc etc! There is no US ranking * 5 = UK ranking, or any other magic formula. Do you think a random company, like the QS world rankings, or THE, are objective in their rankings when they earn money from these rankings through the universities they rank? Do you think the weighting on research and 'reputation' from random surveys is unbiased and representative of every fact? One of the universities I studied at isn't even ranked by QS, yet I had a better academic experience than I had at Penn!
Even comparing acceptance rates is a pitfall. Remember, a student can only apply to one of Oxford or Cambridge. This isn't the case in the US. You cannot look at Oxford's acceptance rates and try to compare it to Harvard. Again, you must meet the minimum requirements to apply to undergraduate programmes in the UK. In the US, there are generally no minimal requirements. A notable amount of people who do not have the minimum requirements apply for many universities as 'dream' or 'reach' schools. In the UK, it's normally one of Oxford or Cambridge and that's it! Again, the US has Early Decision and Early that and this. If you apply Early Decision to some ivies, you can't apply to other universities, and you have a much higher chance of getting accepted. As far as I know the UK just has UCAS. Even the process of applying is completely different. Can this be ignored? I don't think so.
Remember that US universities also recruit students explicitly from certain backgrounds or races to have a diverse student body. Thy are *obsessed* with diversity, and it was obvious not only to me, but to some students themselves at Penn that they had been accepted partly because their background made the school seem more 'diverse'. I don't agree with this practice, when you can go to a university in west Philadelphia and meet almost no African-Americas, but take a look at West Philly... the segregation is bad. On the other hand you can study at Edinburgh and meet few Scottish students...
Here's another huge difference: The US universities you are mainly discussing are private. None of the UK institutions are. Do you think it's fair to make this comparison? If you just start off with comparing public UK and public US universities, you will see a massive difference. What is remarkable is that the UK can deliver a high standard of education to a large portion of its population. The fact that many people get accepted here is a very good thing, and you should be proud of that.
I did at research programme at Oxford with US students from MIT , Harvard, and Oxbridge students. Many of these US students go to Cambridge for their masters in Mathematics, and the Fulbright(to the UK)/Rhodes/Marshall are very popular - do you think this would be the case if nothing in the UK was as good as the US? In addition, I noticed Oxbridge (and even non Oxbridge!) students stand up very well against their US counterparts in that programme.
Do you really think it's only about the university? Maybe the best universities happen to attract the best students. There are smart students everywhere, and given a solid education they will go far. In the UK and the US it is possible to get a good education at a reasonable price, without having to go to a private university. I felt sorry for the students I met at Penn that often commented about their student debt, and had to skip opportunities after graduating to just go work.
It also may be worth looking at the fact that many formally US professors work at US institutions. At Edinburgh, many of the staff came from Stanford, Caltech, MIT etc. When you look at a specific field, like Natural Language Processing, or HIV evolution modelling, you will be very surprised at where the top departments are.