Are you implying that US PhD is superior to European PhD? But the quality eventually depends on the abilities of the researcher in question - not to mention his/her seriousness and passion.
So far as I know, Oxbridge hardly offers any internal funding unless you apply to some country-specific scholarships or external funding bodies - provided that you're eligible. In the event, you get in and they don't offer you funding. Are you willing to self-fund your PhD?