They're about the same for Philosophy and Politics but Warwick is better for Economics. Source: The Complete University Guide.
Personally, I'm not a big fan of 1960s era origin universities (which Warwick is - they can be OK as campuses but boring as somewhere to live) and I find Manchester a city that has too much of a business feel for my liking. Generally, Manchester is pretty highly regarded for sciences, given that it's had more UK Nobel prize winners than anywhere except Oxbridge and UCL, however everyone knows that Warwick is very well regarded for Maths (perhaps a bit too well known given that Imperial, Bristol, and Glasgow rival it).
For the same grade requirements, have you considered Nottingham too? Nottingham's not generally as highly ranked as the others (it used to be a top 10-20 university) but is more highly ranked than Manchester for Economics.