In my opinion the generic InterContinental isn't the equal of the St Regis or Conrad. However there are more InterContinentals than St Regis, and the best of them are the equal of the average Conrads and St Regis's.
In addition there are also a handful of Regent properties. I have no personal knowledge of them, but I get the impression that these are true luxury properties, possibly even higher scale than Conrad and St Regis.