No it's not.
Two very different rates.
Company car is a benefit in kind, the presumption is that all fuel, servicing, tax, insurance and upkeep, as well as depreciation, is paid for by the company, as is fuel, however, if fuel is not, then you can claim the following rates....
HM Revenue & Customs: Company cars - advisory fuel rates from 1 December 2012
Using your own car, which can be provided with a car allowance, is paying you for the fuel and all the other expenses above, hence a much higher rate....
HM Revenue & Customs: Travel - mileage and fuel allowances