The nose design can have an effect on the aircraft but that depends on the type of aircraft.
For small single engine GA aircraft the nose area behind the propellor is critical. Generally known as the cowling over the years it has has many different designs. The varying designs have had drastic effects on engine cooling and drag depending on the plane. Early Mooney's suffered from a less than idea cowling and mods gained them a lot of speed.
For jets like the ones you have pictured there are few things to consider in nose cone design. First off (although this has no aerodynamic effect). There is equipment housed behind the nose cone. Often radar and other things so the nose generally needs to able to accommodate that. Drag is a consideration when designing the nose as well, here is a nice chart regarding the drag on various designs.
There is a pretty lengthy paper on missile design that covers nose cones a bit as well.
For supersonic planes there are other considerations as well such as the shock wave produced and other things that are out of my body of knowledge but Im sure someone here can weigh in. One very interesting nose is that of the Concorde. On one hand it had its awesome moveable system which allowed for greater visibility on takeoff and landing and a more streamline (and heat treated glass) for super sonic flight. But perhaps more interestingly the plane had a serious nose heat issue. They solved this by pumping fuel through the nose as a form of coolant.