Elite American universities known globally for their selectivity, research and Nobel prize winning and glittering alumni;
Harvard, Yale, Chicago, MIT, Stanford, Columbia, Cornell, Caltech, UPenn, Princeton, Dartmouth, Brown, Berkeley, Johns Hopkins.
Elite American Universities which although "world-class" are perhaps not the global heavyweight names as those mentioned above but certainly prestigious within the US;
UCLA, NYU, Texas A&M, UNC; Chapel Hill, USC, UVA, Pittsburgh, Duke, Rice, Georgetown, Michigan, University of Texas Austin, Uniersity of Miami Ohio, Notre Dame, Rutgers, Penn State, Vanderbilt, College of William and Mary, Nothwestern.
Elite UK universities known globally;
Oxford, Cambridge, Imperial, UCL, King's College, Edinburgh
World Class universities with more of a national rep than a global one;
Durham, Bristol, Glasgow, Exeter, York, Warwick and then possibly Manchester and Leeds and St Andrew's
The Ivy Leagues in the US are not necessarily the best 8 in the US but they are certainly amongst the most selective and the oldest in the country hence why the term Ivy League is often associated with academic excellence. All eight of the Ivy Leagues are known world wide as are the rest of the elite US Universities. I mean I would plump for a place at an Ivy League or MIT/Chicago/Stanford over most UK universities perhaps except Oxford or Cambridge.
UCL has produced a number of high profile alumni as has King's and both have world-class reputations for medical research as does Imperial. LSE is second to none really for politics and finance etc. Edinburgh has always had a strong reputation in most fields, has produced PMs, world-class medical faculty which was the inspiration for UPenn's medical school and was part of the "age of enlightenment" which led to Edinburgh being labelled as "The Athens of Northern Europe".
Manchester has had much association with Nobel prize winners but not produced many of their own (i.e. mainly faculty) and Manchester has only reccently come onto the radar through the merger in 2006 but will certainly be up there in the future although I doubt the top 5 will ever change from Oxford, Cambridge, Imperial, LSE, UCL. Then perhaps Edinburgh and King's then Warwick then Manchester.