The purpose of a surge tank is to either reduce high surge pressures or to prevent very low surge pressures. The surge tank does this by having available at all times a calculated amount of liquid and air (or gas) that is connected to the main pipe so that it can either push additional liquid into the pipeline to support the line pressure and prevent low pressure, or accept an inflow of liquid from the line and prevent high pressures.
A bladder type pressure surge tank has an internal membrane, usually made from rubber, that separates the compressible air charge from the liquid at the bottom of the tank, whilst a compressor type pressure surge tank does not.
The membrane prevents absorption of the gas charge by the liquid, so that the gas charge does not have to be re-charged with extra gas.
No, both types of vessels perform exactly the same function with the same effectiveness.
As long as you make sure that the surge engineer who designed the system is involved in the decision it does not matter whether you have a horizontal or vertical pressure surge tank as they will perform the same.
Bladder type tanks are normally considered cheaper to purchase and cheaper to own.
You might choose a compressor controlled pressure surge tank where the pumping condition changes regularly, or you might choose a bladder type pressure surge tank where the equipment is remotely located, or where the there is a shortage of skilled labour to maintain the equipment.