UK vs USA for Geophysics

Which of the following universities would be the best for geophysics? Here are some things that I want from a university in general just to get an idea about what I consider “good”.

It must be challenging (the Caltech type).
I want the course to focus on math/physics as much as possible.
Lots of research.
Smaller is better.

The universities are: UK: Bristol and Southampton
USA: Rice, Wustl, Brown.

On QS rankings, Bristol and Southampton are both much ahead of their US counterparts when it comes to Earth and Marine Sciences, but I do not care if they are better in Geology or Marine sciences and I could not find rankings only for geophysics. At the same time, everybody tells me to go for US, but I want to hear more opinions.

Well, you have to get in first, but subject rankings are a terrible way to look at it as the experience is quite different between England and US.
In England, you only study the subject(s) you sign up for and switching majors is hard. In the US, you don’t declare majors until later and may (and sometimes have to) take classes in a bunch of other subjects. The US has continuous assessment. In the UK, your marks tend to come down to a few big tests at the end of the year.

Rice and Brown are relatively small. UK Unis (besides St. A’s) tend to be bigger, relatively speaking and are publics. All three American Unis you listed are rich elite privates and far harder to get in to that Bristol or Southampton. Undergraduate research (especially at a small rich private uni) is far more typical in the US than in the UK.

Where do you have residency? That will have an effect on costs and fin aid.

If you want a Caltech-type experience (which Rice is closest to delivering), why are you looking at these unis (besides Rice) rather than Cambridge natural science or Caltech or Northwestern ISP?

I am from Romania and I need financial aid (a lot).

These are not all of my choices, here is my full list (I applied for physics/astrophysics to some of these, not only to geophysics):
US:Caltech, Princeton, Yale, Stanford, Brown, Rice, Wustl, Tufts (physics/astrophysics), Emory (physics), Grinnell (physics), Carleton, Colby (physics/astronomy).
UK(geophysics at all of them): UCL (waiting), Edinburgh (waiting), Leeds (waiting), Bristol (got an offer), Southampton (got an offer).

Can you pay for the UK unis? Even though the tuition is really cheap for the Scottish unis, I don’t think you can get scholarships there.

I have some friends at Oxford, Ucl, Edinburgh, and Southampton with the same financial situation as me (earn <$20000/yr) and they told me not to worry about money. I can get a loan for those 9250£ for tuition and pay them over a period of 30 years (you pay as much as you can, after 30 years the remaining dept is erased). The living expenses can get to 12000-15000£, but I am eligible for a financial aid package of 2000-3000£. I remain with 10000-12000£. My parents can pay about 2000£ per year. My dad will sell a part of his heritage (10000£) and the rest will be paid from scholarships, money obtained from work, and another loan. I know I am stretching quite a lot, that is why I hope I will get in a US uni with a big financial aid.

I can get scholarships, but they are not that great. And people as poor as me can get a financial aid of 2000-3000£ per year, as I’ve said above.