Tier 1: Harvard, Yale, Princeton, Oxbridge,
Tier 2: Stanford, MIT, LSE, Imperial,
Tier 3: Chicago, Columbia, Dartmouth, CIT, Berkeley
Tier 4: UCL, NYU, Cornell, Duke, Northwestern
Tier 5: Michigan, UIUC, Carnegie Mellon, UCLA, Brown,
Brown has had its decline IMO - and in the THES rankings opinion. Rhode Scholar is still very very prestigious and the link of harvard - oxford honestly makes the suggestion that they are the same level - also world rankings mostly put oxbridge top 5. Yale even drops out on some of those rankings.
Its also about specialty. LSE is just a propaganda machine but has made it work into a class act and imperial is just such an amazing school at what it does and has been at the forefront of so much and has always been so good.
E.g. I want to go to the Harvard business school but maybe Chicago economics. Post graduate especially it is specialization, but undergrad thats what I feel is wrong with the original table (though the unfamiliar names I have left like CIT).