Traditional thinking used to suggest that a double wishbone setup, with a pair of A-frames, one above the other, would provide better control of the wheel through its movement than a McPherson strut. But a properly set-up strut will work just as well. The deciding factor nowadays tends to involve manufacturing methods and costs and packaging more than perceived benefits in terms of handling or grip.
A McPherson has a single spring/damper unit forming the link from the top of the wheel hub to the car's chassis. The bottom of the hub is joined to the chassis by a variety of methods, all of which can be considered a wishbone, as they link to the chassis at two points to control vertical movement, as well as provide front-to-back location of the hub. This can either be an A-frame or a single swinging arm, with another arm or an anti-roll bar providing longitudinal location.
A double wishbone system, on the other hand, features a pair of A-frames, one above the other, mounted to the top and bottom of the wheel hub. A separate spring/damper unit then sits between either the hub itself or one of the wishbones and the body to control the wheel movement.
Rear suspension can be slightly different, particularly on front-wheel drive cars. There's no need to house a diff or driveshafts, so a cheap and easy way of arranging it is to bolt the wheels at either end of a solid beam axle. This whole axle is then suspended underneath the car and simply goes up and down.
However, a much better system is independent rear suspension, which typically uses either a McPherson arrangement or double wishbones again, depending on what the designers can manage to fit in the physical package.
Typically, the hub can be located by trailing arms, running back from mounting points ahead of the wheel and one from the centre of the car. This then allows each rear wheel to be suspended independently. giving far greater control.