stancioiu, I think we need some more information. From the ATC perspective it's not just a choice between ATC and own navigation. If you are flying a procedural approach you are, by definition, on your own navigation - the answer about changing to a visual approach depends on the air traffic service (if any) that you are receiving. If you are under ATC, you would need to be cleared for a visual approach because ATC still have to separate you from other IFR aircraft.
As to the type of approach, is the difference that the VOR/DME approaches a runway but the circling bit relates to visual manoeuvring following an IAP to a different runway (or a cloudbreak procedure, correctly called an aerodrome approach procedure I think).
Sorry if this is all known to you but I offer it just in case it helps.