Submersible Sump Pumps
Essentially, the size of the sump pit in your basement will determine which pump you select. Because submersible pumps are placed below water, you'll need a bigger pit than with a pedestal pump. The fact these pumps operate underwater provides some nice benefits.
As the pump motor and impeller are underwater, the noise level is reduced. Another benefit of a submersible sump pump is that the water helps to cool the motor, which is especially important during extended periods of use. Think about it, the last thing you want is your pump overheating and breaking down in the middle of a torrential downpour. This is what leads to flooded basements.
If you have a shallow or narrow sump pit, look at a pedestal sump pump instead.
Pedestal Sump Pumps
Pedestal sump pumps are primarily used in situations where the sump pump pit is either narrow, or shallow. Because the entire pump is located above the water of the sump pit, they don't require much space.
Pedestal sump pumps were the residential standard until submersible pumps became more prevalent. Look for a pump made of cast iron, as these will hold up well to the wear and tear of protecting your basement.
If your sump pump pit contains any solids, you'll want to go with a submersible pump instead. Likewise, if the operating noise of your sump pump is a concern, choose a submersible pump instead.