There are a number of reasons why you might be considering using brake shoes rather than brake pads. There is a lot of evidence to suggest that the former is considerably safer than the latter, and most modern cars have a combination of brake shoe in their emergency stop system, as it provides a reliable stop. You do not need to decide between brake shoes and brake pads for a long period, of course, as you can have both within the same car if you want; the two do not interfere with each other, and it is common to use one for the emergency brake, and the other for normal brake patterns.
The main difference between the two different types of brake pads and shoes is their position in the vehicle. The brake shoes are designed to fit inside your drum-style brakes, while brake pads are placed on top of disk brakes, and serve to pressurize these discs when you apply the brakes.
The best reason for using a brake shoe is that it is made from a material which provides friction to the drum. The pad also has some friction, but not nearly as much as in the shoe. This means that, when you need a powerful break, the shoe has the best traction and force, while the pad is likely to be slower to stop. The brake pad uses pressure to force the disk into the car, so you would experience less friction with the pad than the shoe. However, as the pad is also being placed under immense strain, you can expect to see wear and tear on these, as much as on the car itself.
The brake shoe is designed to handle a lot of friction, and the material is hard wearing. You can also easily spot when the shoe is becoming worn, as you will get a weaker stop, with more contact needed on the pedal. This makes it more reliable than the pad, which does not have such a clear warning. While replacing the pad is simpler, and can be managed alone, the shoe generally needs to be replaced less often.
Front or Back
Despite the many advantages of brake shoes, when you are using drum brakes, you will need to have a rear or four wheel drive. These kinds of brakes cannot be used at the front of the car, so if you have front wheel drive cars, where the brakes need to be applied to the front of the car, then you will need to have brake pads, rather than shoes. In addition, you cannot use the two together, so if you have a drum brake vehicle, then you cannot use brake pads on them, and nor can you use disc brakes with brake shoes. Therefore, part of deciding between these two kinds of brakes is knowledge of what your car is capable of, and what kind of drive it has.