The difference of computer power supplies having one or multiple 12V power rails is nothing more than a design differentiation; a differentiation which spurred a real marketing war. Companies which produce units with a single large 12V rail claim that they are more stable and powerful and companies which produce units with multiple 12V rails claim that they are better and safer.
Both of the above claims are inaccurate. Let us start with the multiple rail designs. True enough, they are considered to be safer because overloading any of their 12V lines will cause the over-current protection to kick in and turn off the power supply. True enough, in the occurrence of a catastrophic event which might force most of the power in the circuit being channeled through a single connector, the wires of a very powerful 12V line will be destroyed and might even start a fire. However nearly all high-end PSUs from quality manufacturers with multiple 12V lines are created in such a way that all of their lines far exceed the ATX safety specifications! We have seen for example a power supply with multiple 12V lines and each of them rated at 40A maximum using 16 AWG wires, which wires might be thick for a computer power supply but still are not thick enough to safely transfer 40A for prolonged periods of time.
On the other hand enthusiasts tend to prefer units with a single 12V line because they negate the possibility of a weak 12V line getting overloaded by a single power hungry device. Considering that each individual rail of multiple rail high performance power supply is far stronger than it was supposed to be, this is highly unlikely to happen.
The fact is that whether using one or multiple 12V power lines, a catastrophic even can always take place and cause great damage. All quality manufacturers integrate several safety methods (e.g. OCP circuits) to ensure this does not happen despite the number of rails their apparatus has. And you will never find a very weak 12V rail on a high performance power supply which could cause a power imbalance and force the shut down the unit. Whether shopping for a quality product, both those based on a single rail design and those based on multiple 12V rail designs are pretty much equal.